Estatística e Probabilidade (5)

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Em uma distribuição de probabilidades é necessário:
 P(x) = 1, onde x toma todos valores possíveis
0  P(x)  1 para todo o x.
A distribuição de probabilidades indica a percentagem de vezes que, em grande quantidade de observações, podemos esperar a ocorrência de vários resultados de uma variável aleatória.
Distribuição de Probabilidades
Distribuições de probabilidade
Distribuições descontínuas ou discretas
Distribuições contínuas
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Envolvem distribuições de probabilidades de variáveis aleatórias relativas a dados que podem ser contados.
Exemplos:
 Número de ocorrências por amostras
 Número de ocorrências por unidade num intervalo de tempo
 Número de fumantes presentes em eventos esportivos
Distribuições Descontínuas ou Discretas
Uniforme ou Retangular
Binomial
Binomial Negativa ou de Pascal
Geométrica
Poisson
Multinomial ou Polinomial
Hipergeométrica
Formas da distribuição descontínua
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Quando se usa as distribuições contínuas?
 A variável aleatória discreta apresenta um grande número de resultados;
A variável aleatória em questão é contínua.
Os ponteiros de um relógio podem parar em qualquer dos infinitos pontos do círculo
logo
A probabilidade de parar em um ponto definido é zero
Nas distribuições contínuas utilizam-se a probabilidade da ocorrência em um intervalo P(a < x < b);
Em uma distribuição contínua, a probabilidade é dada pela área contida no intervalo considerado.
Distribuições Contínuas
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DISTRIBUIÇÕES CONTÍNUAS
UNIFORME OU RETANGULAR
NORMAL
BIVARIADA NORMAL
EXPONENCIAL
LOGNORMAL
WEIBULL
QUI-QUADRADO 2
t DE STUDENT
F DE SNEDECOR
GAMA
BETA
ERLANG
( formas)
Distribuições Contínuas
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Um pouco de história
No século XVIII, astrônomos e outros cientistas observaram que medidas repetidas de mensurações como a distância à lua variavam como na figura, quando coletadas em grande número. 
Esta forma gráfica era associada aos erros de mensuração, daí o nome de “Distribuição normal dos erros” e depois “Distribuição normal”
Também é conhecida por “Distribuição Gaussiana”, em função do modelo matemático desenvolvido por Karl F. Gauss para este comportamento.
Distribuição Normal
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Peso da população adulta
n = 5000 µ = 75 kg s = 12 kg
 Altura de universitários
 n = 3000 µ = 152 cm s = 5 cm
Comprimento de uma régua
n = 1000 µ = 30cm s = 0,15cm 
 Pessoas num restaurante 
 µ = 250 por dia s = 20 por dia
Distribuição Normal - Exemplos
Gráf9
		0
		0.0004
		0.0016
		0.0046
		0.011
		0.0268
		0.0554
		0.0978
		0.1404
		0.1602
		0.1592
		0.1478
		0.0972
		0.051
		0.0274
		0.0108
		0.006
		0.0014
		0.0006
		0.0004
Plan1
		0.0		0.2																												156.4		168.9				Bloco		Freqüência																		81.0		Coluna1				Bloco		Freqüência
		1.0		0.3																												147.3		134.9				133		0																		83.7						25		0.00
		2.0		0.3																												148.2		34.0				135		1																		75.3		Média		70.0494467376		30		0.00
		3.0		0.15																												154.9				2		137		2																		48.6		Erro padrão		0.1683163441		35		0.00
		4.0		0.05																												153.3				133		139		7																		61.9		Mediana		70.0633417585		40		0.00
																																150.6				135		141		28																		66.8		Modo		69.0926289684		45		0.01
																																152.9				137		143		56																		94.7		Desvio padrão		11.9017628329		50		0.03
																																151.2				139		145		133																		71.0		Variância da amostra		141.6519585301		55		0.06
																																143.7				141		147		228																		64.7		Curtose		0.1865759888		60		0.10
																																156.0				143		149		369																		91.6		Assimetria		0.0407219811		65		0.14
																																154.4				145		151		387																		64.8		Intervalo		90.8738002181		70		0.16
																																152.0				147		153		503																		85.0		Mínimo		27.2383239865		75		0.16
																																151.4				149		155		454																		61.1		Máximo		118.1121242046		80		0.15
																																146.6				151		157		333																		73.4		Soma		350247.233688242		85		0.10
																																155.2				153		159		252																		69.1		Contagem		5000		90		0.05
																																152.4				155		161		148																		83.0						95		0.03
																																147.6				157		163		61		600		0.20														64.9		90.8738002181				100		0.01
																																148.9				159		165		23		500		0.17														81.7		5				105		0.01
																																160.6				161		167		11		400		0.13														68.4		25				110		0.00
																																149.0				163		169		4		300		0.10														57.4		30				115		0.00
																																148.0				165		Mais		0		200		0.07														66.6		35				120		0.00
		135.7								Bloco		Freqüência																				146.2				167						100		0.03														63.7		40				Mais		0.00
		138.0				167.1				134		0																				152.3				169						3000		1.00														56.4		45						5000
		138.2				135.7				136		1																				152.4																										51.3		50
		138.4				31.4				138		0																				152.4																										60.8		55						0
		139.6		k		20				140		5																				163.2																										77.5		60						2
		139.9		h		1.5717523638				142		16																				145.9																										56.7		65						8
		140.0				2				144		35																				148.2																										81.6		70						23
		140.5		1		134				146		68																				144.4																										66.6		75						55
		140.5		2		136				148		108																				153.2																										59.0		80						134
		140.6		3		138				150		110																				153.8																										76.8		85						277
		140.6		4		140				152		176																				155.4																										53.2		90						489
		140.6		5		142				154		136																				154.7																										68.7		95						702
		140.8		6		144				156		132																				151.5																										61.4		100						801
		140.8		7		146				158		96																				151.1																										74.6		105						796
		140.8		8		148				160		59																				145.3																										61.6		110						739
		141.0		9		150				162		31																				146.4																										62.2		115						486
		141.3		10		152				164		20																				146.8																										68.8		120						255
		141.4		11		154				166		6																				151.2																										74.8								137
		141.4		12		156				168		1																				155.4																										69.4								54
		141.8		13		158				Mais		0																				146.7																										81.9								30
		141.9		14		160																										157.8																										72.7								7
		141.9		15		162																										155.3																										65.9								3
		142.1		16		164																										165.4																										84.8								2
		142.2		17		166																										141.5																										68.7								0
		142.2		18		168																										144.3																										77.2
		142.3																														157.1																										66.2
		142.3																														152.1																										68.8
		142.4																														155.0																										64.8
		142.5																														149.1																										58.1
		142.6																														142.4																										67.8
		142.6																														158.174.8
		142.7																														151.8																										70.2
		142.8																														148.9																										91.1
		142.8																														151.2																										61.2
		142.9																														146.7																										51.6
		142.9																														151.7																										71.1
		143.1																														149.9																										45.2
		143.2																														160.9																										95.2
		143.2																														153.3																										101.2
		143.3																														148.4																										63.8
		143.4																														160.5																										75.8
		143.4																														154.0																										52.6
		143.5																														149.7																										68.4
		143.6																														151.6																										79.7
		143.6																														155.4																										74.6
		143.7																														155.6																										52.3
		143.7																														152.7																										64.4
		143.7																														157.8																										34.6
		143.8																														155.9																										61.5
		143.8																														146.6																										68.3
		143.8																														148.3																										64.8
		143.9																														155.8																										85.2
		143.9																														149.2																										79.1
		143.9																														144.1																										56.3
		144.0																														144.2																										69.5
		144.0																														159.8																										72.1
		144.0																														155.2																										58.1
		144.1																														147.6																										66.8
		144.1																														148.3																										71.3
		144.1																														153.5																										69.0
		144.2																														151.5																										64.5
		144.2																														158.0																										55.6
		144.3																														148.9																										66.6
		144.3																														144.4																										88.8
		144.3																														153.4																										77.0
		144.3																														149.8																										86.8
		144.4																														145.3																										75.7
		144.4																														152.9																										84.7
		144.4																														156.0																										70.1
		144.6																														157.7																										62.7
		144.6																														155.2																										77.3
		144.7																														149.4																										80.1
		144.7																														144.6																										71.7
		144.7																														143.0																										47.9
		144.7																														158.1																										89.1
		144.7																														160.5																										88.1
		144.8																														154.9																										42.2
		144.8																														151.8																										69.8
		144.8																														153.6																										82.7
		144.9																														152.6																										98.4
		144.9																														150.9																										68.3
		145.0																														152.6																										68.6
		145.0																														152.0																										45.1
		145.0																														149.4																										92.5
		145.0																														147.3																										65.9
		145.1																														151.1																										64.9
		145.1																														151.9																										78.5
		145.1																														144.2																										71.8
		145.1																														158.4																										59.7
		145.1																														157.1																										86.5
		145.2																														155.1																										58.2
		145.2																														163.4																										80.7
		145.2																														154.3																										65.8
		145.2																														147.1																										74.4
		145.2																														155.5																										59.5
		145.2																														147.6																										67.1
		145.3																														155.0																										75.7
		145.3																														155.0																										56.3
		145.3																														144.7																										65.8
		145.3																														160.2																										60.3
		145.3																														147.5																										75.2
		145.3																														152.6																										80.3
		145.3																														155.6																										84.7
		145.4																														146.4																										72.0
		145.4																														153.5																										91.3
		145.4																														164.6																										64.3
		145.4																														144.7																										74.5
		145.4																														152.8																										86.5
		145.5																														151.3																										69.9
		145.5																														153.5																										74.1
		145.5																														151.6																										90.5
		145.6																														157.8																										57.3
		145.6																														144.7																										72.1
		145.6																														156.5																										68.3
		145.7																														150.1																										70.0
		145.7																														153.7																										67.9
		145.7																														145.0																										69.5
		145.7																														151.6																										83.4
		145.7																														155.4																										65.0
		145.8																														148.7																										80.9
		145.8																														147.3																										85.5
		145.8																														147.2																										101.9
		145.9																														148.2																										67.4
		145.9																														152.0																										65.3
		146.0																														148.1																										73.1
		146.0																														149.1																										63.7
		146.0																														150.1																										68.1
		146.0																														145.8																										44.6
		146.1																														145.6																										77.4
		146.1																														150.9																										68.4
		146.1																														160.5																										72.4
		146.2																														149.0																										64.4
		146.2																														155.8																										62.9
		146.2																														151.7																										71.0
		146.2																														151.7																										82.9
		146.2																														153.3																										76.5
		146.2																														147.783.2
		146.2																														141.9																										64.0
		146.3																														153.8																										75.1
		146.3																														148.1																										75.0
		146.3																														150.8																										72.2
		146.3																														160.9																										65.7
		146.3																														159.0																										62.4
		146.3																														153.8																										79.6
		146.3																														154.6																										85.2
		146.3																														150.5																										81.9
		146.3																														154.8																										78.5
		146.4																														147.7																										71.9
		146.4																														161.2																										71.0
		146.4																														152.6																										78.4
		146.4																														160.4																										65.9
		146.5																														151.0																										57.5
		146.5																														145.8																										56.0
		146.5																														155.9																										65.2
		146.5																														143.7																										67.5
		146.5																														150.0																										90.2
		146.6																														155.4																										74.2
		146.6																														151.3																										71.1
		146.7																														154.8																										48.5
		146.7																														145.8																										64.0
		146.7																														146.3																										71.1
		146.7																														151.7																										56.2
		146.7																														155.5																										81.5
		146.8																														155.4																										91.0
		146.8																														148.4																										66.2
		146.8																														159.3																										72.2
		146.8																														149.4																										71.6
		146.8																														153.7																										76.9
		146.9																														149.1																										103.5
		146.9																														158.1																										49.5
		146.9																														152.5																										56.6
		146.9																														150.3																										42.1
		146.9																														151.8																										93.5
		146.9																														146.0																										76.1
		146.9																														151.5																										90.0
		146.9																														153.8																										74.6
		146.9																														146.5																										69.4
		147.0																														161.1																										76.8
		147.0																														154.4																										81.2
		147.0																														160.4																										71.7
		147.0																														147.7																										60.0
		147.0																														156.6																										59.8
		147.0																														157.7																										70.8
		147.1																														152.0																										78.3
		147.1																														146.5																										69.6
		147.1																														153.3																										64.6
		147.1																														154.9																										64.7
		147.2																														148.4																										67.6
		147.2																														150.5																										65.4
		147.2																														153.5																										90.3
		147.2																														146.8																										67.8
		147.2																														152.0																										60.5
		147.3																														145.5																										71.4
		147.3																														148.9																										52.2
		147.3																														154.0																										74.9
		147.3																														145.6																										78.7
		147.3																														153.5																										63.6
		147.3																														160.4																										59.2
		147.3																														150.2																										67.5
		147.3																														147.5																										70.4
		147.4																														149.1																										84.2
		147.4																														154.0																										60.5
		147.5																														157.0																										60.7
		147.5																														165.1																										76.4
		147.5																														161.5																										77.3
		147.5																														151.3																										81.1
		147.5																														148.1																										77.2
		147.6																														154.8																										83.4
		147.6																														146.4																										58.1
		147.6																														152.8																										80.3
		147.6																														152.2																										77.9
		147.6																														150.7																										70.0
		147.6																														152.5																										68.9
		147.7																														148.4																										70.9
		147.7																														159.6																										47.3
		147.7																														151.4																										62.1
		147.7																														153.5																										67.1
		147.7																														156.8																										91.4
		147.8																														158.6																										64.7
		147.8																														151.0																										68.2
		147.8																														153.2																										85.9
		147.8																														152.9																										64.2
		147.8																														153.6																										72.4
		147.9																														153.9																										52.3
		147.9																														148.2																										98.0
		147.9																														151.1																										81.9
		147.9																														161.3																										73.9
		147.9																														153.0																										63.3
		148.0																														150.7																										74.5
		148.0																														150.5																										80.1
		148.0																														150.6																										68.0
		148.0																														148.3																										67.2
		148.0																														152.0																										80.8
		148.0																														153.9																										58.7
		148.0																														156.2																										56.4
		148.0																														153.6																										66.6
		148.1																														153.0																										56.9
		148.1																														145.4																										53.3
		148.1																														168.9																										81.0
		148.1																														154.8																										96.7
		148.2																														150.0																										71.8
		148.2																														151.4																										69.9
		148.2																														153.673.1
		148.2																														152.6																										66.9
		148.2																														147.2																										71.8
		148.2																														152.2																										62.2
		148.2																														148.2																										73.7
		148.2																														149.0																										75.2
		148.2																														156.5																										51.7
		148.3																														159.6																										88.0
		148.3																														151.1																										74.3
		148.3																														154.5																										73.6
		148.3																														149.4																										78.1
		148.3																														157.1																										71.0
		148.3																														155.6																										100.6
		148.3																														159.1																										73.8
		148.3																														153.3																										84.0
		148.3																														157.9																										74.6
		148.3																														147.7																										65.0
		148.3																														162.8																										94.0
		148.3																														151.5																										64.0
		148.4																														156.6																										100.1
		148.4																														156.4																										55.1
		148.4																														155.9																										56.5
		148.4																														146.8																										84.4
		148.4																														151.8																										87.4
		148.5																														156.5																										53.8
		148.5																														149.4																										73.8
		148.5																														150.7																										79.5
		148.5																														140.1																										92.1
		148.6																														148.7																										31.5
		148.6																														152.6																										90.3
		148.6																														149.9																										52.6
		148.6																														147.9																										81.7
		148.6																														152.9																										70.3
		148.7																														161.6																										57.9
		148.7																														154.2																										46.0
		148.7																														147.0																										49.1
		148.8																														151.8																										72.2
		148.8																														138.5																										67.5
		148.8																														158.0																										68.2
		148.8																														154.3																										72.1
		148.8																														148.8																										70.2
		148.8																														150.2																										68.9
		148.8																														156.4																										73.3
		148.9																														155.6																										75.8
		148.9																														157.1																										76.4
		148.9																														155.1																										47.8
		148.9																														148.8																										37.9
		148.9																														156.7																										66.3
		148.9																														161.5																										67.6
		148.9																														153.7																										59.7
		149.0																														145.3																										68.9
		149.0																														154.3																										70.2
		149.0																														154.5																										69.4
		149.0																														158.1																										80.2
		149.0																														150.0																										89.3
		149.1																														144.7																										56.7
		149.1																														151.2																										65.8
		149.1																														153.4																										83.5
		149.1																														160.3																										71.3
		149.1																														158.3																										56.3
		149.2																														145.2																										72.0
		149.2																														146.4																										56.4
		149.2																														153.0																										84.7
		149.2																														154.0																										70.7
		149.3																														144.5																										73.7
		149.3																														155.4																										72.7
		149.3																														142.8																										75.2
		149.3																														151.4																										76.0
		149.3																														145.8																										76.1
		149.4																														154.5																										64.9
		149.4																														158.4																										63.2
		149.4																														145.3																										83.2
		149.4																														152.5																										60.0
		149.4																														148.9																										66.5
		149.5																														156.7																										69.6
		149.6																														151.1																										100.6
		149.6																														156.3																										62.7
		149.6																														152.3																										82.4
		149.6																														146.2																										88.6
		149.6																														155.4																										71.6
		149.7																														145.6																										71.1
		149.7																														150.5																										60.1
		149.7																														161.5																										71.8
		149.7																														146.0																										61.1
		149.7																														155.5																										56.1
		149.7																														153.5																										91.7
		149.8																														145.8																										74.5
		149.8																														153.0																										55.6
		149.8																														150.6																										61.9
		149.8																														154.0																										69.7
		149.8																														146.9																										71.6
		149.8																														148.7																										66.0
		149.8																														148.8																										65.3
		149.9																														151.2																										62.6
		149.9																														151.4																										92.8
		149.9																														159.4																										86.5
		149.9																														136.7																										54.9
		149.9																														152.0																										67.3
		150.0																														153.9																										72.5
		150.0																														151.5																										59.2
		150.0																														146.8																										64.5
		150.0																														151.2																										75.1
		150.0																														156.9																										56.8
		150.0																														151.9																										68.9
		150.0																														152.8																										49.6
		150.0																														156.1																										76.7
		150.0																														151.875.4
		150.0																														155.2																										82.4
		150.0																														148.5																										79.9
		150.0																														155.7																										49.2
		150.1																														139.6																										49.1
		150.1																														150.9																										65.6
		150.1																														152.4																										66.3
		150.1																														153.4																										59.1
		150.1																														147.9																										64.6
		150.1																														145.5																										60.3
		150.1																														150.6																										56.9
		150.1																														145.3																										71.7
		150.1																														150.4																										67.3
		150.2																														151.7																										82.2
		150.2																														152.5																										52.3
		150.2																														144.8																										78.5
		150.2																														149.8																										61.7
		150.2																														150.2																										74.9
		150.2																														147.8																										76.5
		150.3																														151.3																										71.3
		150.3																														148.2																										51.7
		150.3																														151.2																										47.3
		150.3																														150.8																										58.6
		150.3																														150.4																										61.9
		150.3																														149.7																										57.4
		150.3																														142.9																										74.4
		150.3																														149.6																										64.5
		150.3																														150.1																										49.6
		150.4																														153.0																										63.8
		150.4																														152.0																										75.3
		150.4																														155.8																										66.0
		150.4																														157.0																										75.0
		150.4																														149.4																										77.6
		150.4																														150.0																										79.7
		150.4																														150.6																										85.2
		150.4																														162.3																										94.7
		150.4																														154.0																										68.3
		150.4																														157.6																										74.1
		150.4																														150.5																										75.2
		150.4																														148.4																										60.1
		150.4																														149.4																										79.5
		150.5																														150.1																										74.8
		150.5																														153.6																										58.1
		150.5																														151.1																										87.4
		150.5																														161.8																										68.3
		150.5																														151.9																										90.4
		150.5																														158.5																										59.1
		150.5																														143.7																										83.1
		150.5																														147.9																										64.8
		150.5																														148.9																										55.5
		150.6																														162.2																										70.9
		150.6																														147.3																										70.8
		150.6																														145.3																										76.0
		150.6																														157.4																										71.0
		150.6																														151.5																										51.5
		150.6																														143.7																										74.2
		150.6																														148.7																										43.2
		150.6																														156.2																										65.5
		150.6																														162.4																										54.3
		150.6																														153.2																										70.9
		150.6																														158.8																										84.6
		150.7																														161.7																										68.3
		150.7																														155.9																										71.6
		150.7																														157.3																										66.1
		150.7																														148.0																										71.0
		150.8																														154.6																										70.4
		150.8																														147.2																										77.6
		150.8																														154.4																										68.3
		150.8																														154.6																										51.7
		150.8																														151.2																										84.3
		150.8																														159.2																										58.3
		150.8																														154.6																										62.0
		150.8																														147.2																										61.2
		150.8																														150.9																										87.4
		150.8																														147.0																										65.5
		150.8																														156.5																										81.4
		150.8																														154.0																										77.6
		150.9																														154.0																										77.5
		150.9																														154.2																										93.1
		150.9																														149.1																										84.2
		150.9																														159.3																										80.2
		150.9																														156.5																										41.3
		150.9																														149.8																										61.7
		150.9																														154.4																										60.0
		150.9																														146.7																										58.4
		150.9																														147.2																										78.3
		151.0																														152.3																										49.7
		151.0																														155.2																										41.7
		151.0																														144.4																										55.8
		151.0																														147.0																										78.3
		151.0																														147.0																										72.2
		151.0																														150.2																										72.3
		151.0																														152.5																										78.7
		151.0																														145.3																										66.9
		151.0																														149.9																										100.9
		151.0																														156.2																										84.4
		151.0																														152.8																										59.3
		151.1																														143.1																										83.8
		151.1																														146.4																										34.8
		151.1																														151.4																										73.5
		151.1																														154.6																										73.1
		151.1																														155.1																										62.2
		151.1																														152.9																										74.6
		151.1																														163.9																										60.9
		151.1																														146.0																										61.5
		151.1																														152.8																										71.3
		151.2																														149.967.5
		151.2																														151.2																										67.7
		151.2																														144.4																										50.6
		151.2																														149.0																										56.0
		151.2																														147.4																										83.1
		151.2																														138.4																										80.5
		151.2																														142.8																										87.9
		151.2																														153.7																										79.1
		151.2																														153.8																										80.2
		151.2																														143.8																										90.2
		151.2																														150.5																										72.3
		151.3																														153.4																										75.4
		151.3																														145.2																										67.8
		151.3																														147.6																										76.7
		151.3																														155.7																										75.6
		151.3																														149.6																										68.2
		151.3																														152.3																										60.6
		151.3																														157.1																										49.9
		151.3																														144.0																										73.0
		151.3																														149.3																										80.5
		151.3																														150.2																										56.6
		151.4																														147.5																										57.1
		151.4																														145.5																										55.7
		151.4																														150.3																										84.3
		151.4																														151.9																										86.3
		151.4																														158.1																										53.4
		151.4																														145.5																										71.1
		151.5																														153.8																										72.1
		151.5																														158.7																										89.2
		151.5																														153.4																										86.1
		151.5																														157.7																										75.2
		151.5																														158.3																										58.8
		151.5																														147.1																										72.4
		151.5																														152.5																										62.9
		151.6																														155.5																										89.3
		151.6																														159.4																										77.1
		151.6																														159.0																										63.8
		151.6																														163.0																										71.3
		151.6																														151.6																										62.7
		151.6																														145.9																										38.7
		151.6																														160.9																										76.0
		151.6																														150.6																										72.3
		151.6																														154.9																										79.6
		151.6																														154.8																										88.0
		151.6																														156.6																										71.1
		151.6																														154.3																										101.6
		151.7																														156.2																										59.9
		151.7																														148.3																										58.4
		151.7																														151.0																										45.4
		151.7																														149.5																										60.4
		151.7																														161.6																										81.1
		151.8																														149.4																										73.1
		151.8																														159.0																										67.9
		151.8																														142.6																										99.9
		151.8																														161.0																										43.9
		151.8																														151.8																										76.5
		151.8																														146.4																										60.8
		151.9																														153.4																										82.3
		151.9																														148.8																										56.4
		151.9																														149.9																										63.2
		151.9																														154.2																										85.2
		151.9																														153.3																										44.5
		151.9																														152.8																										75.0
		152.0																														149.0																										74.9
		152.0																														149.5																										72.8
		152.0																														150.4																										65.7
		152.0																														147.6																										78.0
		152.0																														151.9																										79.6
		152.0																														152.6																										78.9
		152.0																														152.3																										84.9
		152.0																														153.2																										75.0
		152.1																														151.3																										68.1
		152.1																														163.7																										87.6
		152.1																														157.3																										62.6
		152.1																														160.9																										68.7
		152.2																														149.4																										81.2
		152.2																														152.3																										77.7
		152.2																														138.2																										44.2
		152.2																														162.2																										68.7
		152.3																														154.1																										81.9
		152.3																														156.8																										70.2
		152.3																														142.6																										78.1
		152.3																														154.7																										75.1
		152.3																														146.5																										65.6
		152.3																														148.6																										66.6
		152.4																														158.6																										60.0
		152.4																														155.0																										82.9
		152.4																														160.3																										75.1
		152.4																														152.9																										60.4
		152.4																														149.3																										64.0
		152.4																														151.4																										67.6
		152.4																														148.9																										70.9
		152.5																														155.5																										66.6
		152.5																														152.4																										57.7
		152.6																														155.1																										74.1
		152.6																														149.8																										93.5
		152.6																														145.3																										78.3
		152.7																														148.6																										51.1
		152.7																														155.2																										72.1
		152.7																														145.5																										61.3
		152.7																														157.6																										79.5
		152.7																														151.4																										71.9
		152.7																														147.4																										60.4
		152.7																														153.0																										94.2
		152.7																														145.1																										51.4
		152.7																														153.5																										74.2
		152.7																														156.844.4
		152.7																														151.4																										63.8
		152.8																														147.5																										67.9
		152.8																														152.1																										81.7
		152.8																														152.7																										70.3
		152.8																														146.6																										70.7
		152.8																														150.9																										77.6
		152.8																														149.6																										77.7
		152.9																														152.9																										56.3
		152.9																														144.6																										64.4
		152.9																														155.2																										71.0
		153.0																														158.7																										67.8
		153.0																														150.1																										85.6
		153.0																														146.5																										61.4
		153.0																														140.0																										76.0
		153.0																														153.6																										62.8
		153.0																														157.0																										61.4
		153.0																														147.3																										53.1
		153.0																														148.0																										64.6
		153.1																														152.1																										81.7
		153.1																														149.6																										63.5
		153.1																														152.0																										62.6
		153.1																														151.7																										84.4
		153.1																														151.6																										57.6
		153.1																														154.2																										63.8
		153.1																														147.6																										73.9
		153.1																														157.0																										84.5
		153.1																														146.3																										58.9
		153.1																														150.4																										64.5
		153.1																														149.1																										75.6
		153.1																														148.7																										58.4
		153.2																														157.9																										76.1
		153.2																														160.3																										75.5
		153.2																														152.6																										92.8
		153.2																														159.1																										48.9
		153.2																														143.9																										67.7
		153.2																														147.2																										76.6
		153.2																														163.5																										68.2
		153.3																														151.4																										63.4
		153.3																														152.1																										75.3
		153.3																														156.2																										98.4
		153.3																														154.3																										66.6
		153.3																														159.0																										67.6
		153.4																														154.2																										61.8
		153.4																														147.9																										75.9
		153.4																														147.1																										51.3
		153.4																														149.0																										43.4
		153.4																														149.7																										91.2
		153.4																														152.1																										59.0
		153.4																														144.4																										66.1
		153.4																														148.4																										74.9
		153.4																														147.2																										69.6
		153.5																														154.1																										73.7
		153.5																														163.2																										81.9
		153.5																														145.7																										64.8
		153.5																														150.9																										81.5
		153.6																														147.1																										73.9
		153.6																														151.6																										59.7
		153.6																														153.1																										74.7
		153.6																														151.3																										62.1
		153.6																														155.6																										75.5
		153.6																														144.2																										78.4
		153.6																														147.4																										82.9
		153.6																														158.2																										82.7
		153.6																														157.2																										68.1
		153.7																														148.5																										54.4
		153.7																														141.3																										45.9
		153.7																														143.6																										74.8
		153.7																														157.6																										75.3
		153.7																														149.4																										92.1
		153.7																														159.1																										63.5
		153.7																														162.1																										68.2
		153.7																														152.3																										81.2
		153.7																														156.5																										55.4
		153.8																														151.9																										74.6
		153.8																														149.8																										56.5
		153.8																														144.5																										48.2
		153.8																														160.8																										87.1
		153.8																														157.7																										50.1
		153.8																														146.8																										98.3
		153.8																														151.3																										74.2
		153.8																														148.4																										70.0
		153.8																														147.7																										65.5
		153.8																														154.2																										68.0
		153.8																														152.2																										84.3
		153.8																														155.8																										57.2
		153.9																														148.7																										96.6
		153.9																														151.4																										76.3
		153.9																														149.5																										102.1
		153.9																														159.3																										80.7
		153.9																														150.6																										75.8
		154.0																														156.5																										61.0
		154.0																														149.8																										61.0
		154.0																														148.4																										72.5
		154.0																														147.4																										62.9
		154.0																														158.9																										89.4
		154.1																														161.9																										52.5
		154.1																														151.7																										73.0
		154.1																														158.7																										83.5
		154.1																														150.9																										64.1
		154.1																														146.0																										63.9
		154.1																														160.3																										74.2
		154.1																														151.1																										66.6
		154.2																														146.4																										65.2
		154.2																														155.8																										93.7
		154.2																														153.4																										76.3
		154.3																														149.681.9
		154.3																														153.2																										68.9
		154.3																														146.2																										49.1
		154.3																														148.2																										79.1
		154.3																														160.5																										60.2
		154.4																														158.1																										66.7
		154.4																														152.3																										79.1
		154.4																														149.0																										60.3
		154.4																														153.4																										67.6
		154.4																														154.7																										86.1
		154.4																														144.1																										73.8
		154.4																														153.8																										79.7
		154.5																														157.9																										62.3
		154.5																														140.6																										78.4
		154.5																														145.6																										74.6
		154.5																														157.1																										46.7
		154.5																														154.2																										74.0
		154.6																														147.9																										67.9
		154.6																														151.5																										60.8
		154.6																														158.1																										75.5
		154.6																														148.4																										54.3
		154.6																														148.8																										59.9
		154.6																														154.1																										57.1
		154.6																														151.5																										50.9
		154.6																														147.8																										54.8
		154.6																														153.6																										53.3
		154.6																														155.7																										80.0
		154.6																														153.3																										57.1
		154.7																														148.7																										78.6
		154.7																														150.7																										54.2
		154.7																														152.2																										72.1
		154.7																														151.6																										45.7
		154.8																														150.6																										74.3
		154.8																														154.3																										71.1
		154.8																														160.8																										53.9
		154.8																														151.1																										77.0
		154.8																														149.9																										67.7
		154.8																														150.2																										72.8
		154.8																														152.8																										71.4
		154.8																														142.1																										85.9
		154.8																														146.9																										84.9
		154.8																														152.2																										51.2
		154.8																														156.9																										75.4
		154.9																														146.4																										71.5
		154.9																														152.9																										54.5
		154.9																														152.5																										67.4
		154.9																														151.2																										73.1
		154.9																														155.7																										46.0
		154.9																														142.1																										57.5
		155.0																														145.6																										55.2
		155.0																														160.0																										58.9
		155.0																														158.2																										77.2
		155.0																														163.5																										70.6
		155.1																														148.7																										61.9
		155.1																														147.1																										94.8
		155.1																														154.6																										76.2
		155.1																														153.8																										62.7
		155.1																														154.1																										71.8
		155.1																														145.8																										73.6
		155.1																														154.6																										64.5
		155.1																														149.7																										56.1
		155.1																														148.7																										80.2
		155.1																														153.0																										70.6
		155.1																														145.7																										72.9
		155.1																														158.1																										77.8
		155.2																														149.7																										71.3
		155.2																														153.0																										82.2
		155.2																														156.9																										44.7
		155.2																														151.7																										58.7
		155.2																														150.8																										68.2
		155.2																														148.7																										75.4
		155.3																														153.7																										74.7
		155.3																														154.0																										82.0
		155.3																														157.3																										87.3
		155.3																														156.8																										57.0
		155.3																														152.9																										65.1
		155.3																														153.2																										94.9
		155.3																														152.3																										69.7
		155.3																														145.9																										74.8
		155.3																														152.5																										74.7
		155.3																														147.6																										89.4
		155.3																														152.2																										67.2
		155.3																														162.6																										85.7
		155.3																														158.5																										71.9
		155.4																														155.2																										63.1
		155.4																														148.9																										57.2
		155.4																														153.7																										76.7
		155.4																														161.8																										67.4
		155.4																														146.5																										91.1
		155.4																														144.0																										61.6
		155.4																														156.2																										70.4
		155.5																														151.4																										59.3
		155.5																														148.0																										76.9
		155.5																														147.5																										97.4
		155.5																														155.2																										70.4
		155.6																														151.7																										73.0
		155.6																														146.5																										82.8
		155.6																														156.7																										72.6
		155.6																														150.4																										62.0
		155.7																														151.9																										53.4
		155.7																														152.1																										68.6
		155.7																														158.9																										58.9
		155.7																														148.0																										75.4
		155.7																														152.3																										58.2
		155.8																														145.5																										65.8
		155.8																														140.0																										69.0
		155.8																														151.167.2
		155.8																														145.0																										62.0
		155.8																														157.2																										86.6
		155.9																														151.7																										60.2
		155.9																														157.2																										66.8
		155.9																														148.9																										67.7
		155.9																														144.7																										78.2
		155.9																														165.0																										66.5
		155.9																														147.4																										69.5
		156.0																														150.0																										59.3
		156.0																														151.1																										74.7
		156.0																														154.5																										64.6
		156.0																														146.7																										61.5
		156.0																														150.0																										78.1
		156.0																														155.4																										79.4
		156.0																														157.5																										71.2
		156.0																														159.2																										70.4
		156.0																														157.7																										84.6
		156.0																														147.2																										64.3
		156.1																														155.0																										72.4
		156.1																														153.9																										46.2
		156.1																														157.1																										83.3
		156.1																														153.3																										77.5
		156.1																														163.9																										75.4
		156.1																														147.1																										71.0
		156.2																														148.1																										69.7
		156.2																														147.8																										80.1
		156.2																														156.1																										68.7
		156.2																														160.2																										81.7
		156.2																														150.7																										80.6
		156.3																														153.7																										72.7
		156.3																														156.2																										71.1
		156.3																														150.7																										57.9
		156.4																														152.6																										70.4
		156.4																														159.0																										68.4
		156.4																														159.6																										59.5
		156.4																														148.8																										58.9
		156.5																														150.1																										70.0
		156.5																														155.0																										64.8
		156.5																														153.6																										114.9
		156.5																														152.6																										63.1
		156.5																														151.3																										78.0
		156.6																														154.2																										67.8
		156.6																														160.1																										74.8
		156.6																														154.0																										61.6
		156.6																														146.9																										85.9
		156.6																														154.8																										66.6
		156.6																														154.2																										78.7
		156.6																														162.2																										88.0
		156.7																														155.3																										77.9
		156.7																														145.2																										61.2
		156.7																														151.2																										85.8
		156.7																														157.9																										63.8
		156.7																														155.5																										84.7
		156.8																														159.6																										57.7
		156.8																														147.2																										77.0
		156.8																														147.0																										59.9
		156.8																														153.5																										92.0
		156.8																														165.5																										62.8
		156.9																														163.2																										65.0
		156.9																														158.1																										61.2
		156.9																														148.4																										74.0
		156.9																														152.6																										75.5
		156.9																														153.1																										85.8
		156.9																														160.0																										64.8
		156.9																														154.0																										70.6
		157.0																														141.3																										74.3
		157.0																														151.8																										69.4
		157.0																														157.8																										57.5
		157.0																														151.7																										76.2
		157.0																														150.3																										69.4
		157.0																														139.3																										55.9
		157.1																														152.1																										89.8
		157.1																														147.5																										71.5
		157.1																														155.1																										88.2
		157.1																														152.1																										66.7
		157.1																														143.2																										59.3
		157.1																														142.1																										77.8
		157.2																														150.6																										68.5
		157.2																														153.2																										56.8
		157.2																														157.3																										65.8
		157.2																														153.7																										61.0
		157.3																														152.3																										63.5
		157.3																														158.5																										76.5
		157.3																														159.0																										66.6
		157.3																														141.8																										80.8
		157.3																														158.8																										86.8
		157.4																														148.3																										71.4
		157.4																														161.9																										48.6
		157.5																														144.9																										66.9
		157.5																														163.2																										69.1
		157.5																														151.6																										63.3
		157.6																														150.2																										77.1
		157.6																														149.4																										63.7
		157.6																														149.5																										81.3
		157.6																														148.6																										61.7
		157.7																														154.1																										58.7
		157.7																														157.2																										81.1
		157.7																														142.4																										54.6
		157.7																														154.9																										70.5
		157.8																														146.1																										61.4
		157.8																														153.2																										69.7
		157.8																														150.2																										44.5
		157.9																														149.2																										70.6
		157.9																														158.0																										67.4
		157.9																														150.0																										51.1
		157.9																														152.449.0
		157.9																														157.1																										60.2
		157.9																														145.2																										64.3
		157.9																														157.5																										79.0
		158.0																														149.6																										75.5
		158.0																														149.1																										79.1
		158.1																														157.2																										75.6
		158.1																														158.1																										91.3
		158.1																														154.4																										83.7
		158.2																														155.5																										56.3
		158.2																														146.5																										54.0
		158.2																														155.3																										68.4
		158.2																														151.9																										84.0
		158.2																														153.1																										83.9
		158.2																														153.9																										55.7
		158.2																														155.6																										81.3
		158.2																														159.0																										70.5
		158.3																														148.5																										58.7
		158.4																														153.2																										88.5
		158.4																														146.7																										58.4
		158.4																														152.2																										62.1
		158.4																														147.9																										56.6
		158.4																														152.7																										59.5
		158.5																														150.4																										56.1
		158.5																														151.9																										91.3
		158.5																														149.2																										57.5
		158.5																														149.7																										57.2
		158.6																														160.5																										42.7
		158.6																														148.4																										80.2
		158.6																														146.7																										84.1
		158.6																														158.5																										84.4
		158.6																														151.8																										84.8
		158.7																														153.8																										56.5
		158.7																														152.0																										58.7
		158.7																														151.8																										75.0
		158.8																														157.4																										58.3
		158.8																														147.6																										80.5
		158.9																														159.2																										76.9
		158.9																														154.3																										48.3
		158.9																														153.7																										77.4
		158.9																														151.1																										83.6
		158.9																														153.8																										77.0
		158.9																														156.8																										42.7
		159.0																														149.5																										61.6
		159.0																														155.7																										85.5
		159.0																														147.4																										65.3
		159.0																														153.4																										79.6
		159.2																														153.7																										68.4
		159.2																														147.8																										52.4
		159.2																														150.0																										62.8
		159.2																														155.1																										63.7
		159.3																														153.2																										61.1
		159.3																														160.2																										60.8
		159.4																														150.7																										50.5
		159.4																														142.5																										59.1
		159.5																														148.7																										63.2
		159.5																														153.2																										84.8
		159.6																														157.2																										73.9
		159.8																														155.2																										65.7
		159.8																														144.8																										50.0
		159.9																														154.2																										77.2
		159.9																														155.8																										79.5
		160.0																														147.9																										82.6
		160.0																														160.1																										81.3
		160.0																														149.3																										56.6
		160.0																														138.7																										78.8
		160.0																														156.5																										46.7
		160.1																														151.7																										77.9
		160.4																														157.2																										73.6
		160.4																														148.2																										85.4
		160.4																														151.3																										83.5
		160.5																														155.8																										69.4
		160.6																														149.3																										77.0
		160.6																														148.6																										68.1
		160.7																														147.6																										70.8
		160.8																														150.4																										64.3
		160.8																														140.6																										84.8
		160.9																														151.7																										69.9
		160.9																														154.7																										75.8
		160.9																														150.8																										73.6
		161.0																														158.1																										64.4
		161.0																														157.0																										62.9
		161.0																														156.7																										36.2
		161.1																														155.5																										57.0
		161.2																														152.3																										42.0
		161.3																														149.4																										66.8
		161.5																														158.6																										61.0
		161.7																														149.0																										64.6
		161.7																														147.7																										53.5
		161.7																														146.0																										73.5
		161.7																														152.1																										57.7
		161.7																														155.5																										49.3
		161.8																														152.1																										76.5
		161.8																														158.9																										77.3
		161.9																														156.9																										54.1
		162.0																														157.1																										79.8
		162.2																														150.5																										69.9
		162.2																														160.4																										84.4
		162.2																														153.2																										30.0
		162.2																														151.6																										108.3
		162.2																														149.4																										85.7
		162.3																														151.1																										58.4
		162.4																														154.3																										85.3
		162.4																														140.4																										63.6
		162.4																														151.3																										66.2
		162.6																														149.3																										74.6
		162.6																														149.7