MEstII AD1 Gabarito 2018.2

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AD1 – Me´todos Estat´ısticos II – 2/2018GABARITO
Questa˜o 1A´rea sob a curva e´ a a´rea de um triaˆngulo:12 · 5 · k = 1⇒ k = 0, 4
Questa˜o 2Segmento de reta determinado pelos pontos (0; 0) e (5; 0, 4) ∴ y = bx .
0, 4 = 5b =⇒ b = 0, 08
f (x) = 0, 08x 0 ≤ x ≤ 5
Questa˜o 3P(X > 2 |X < 4) = P(2 < X < 4)P(X < 4)
P(2 < X < 4) = f (2) + f (4)2 × 2 =f (2) + f (4) = 0, 08 · 2 + 0, 08 · 4 = 0, 48
P(X < 4) = 12 · 4 · f (4) = 2 · f (4) = 2 · 0, 08 · 4 = 0, 64
P(X > 2 |X < 4) = P(2 < X < 4)P(X < 4) = 0, 480, 64 = 0, 75
AD1 – MEstII – 1/2018 1
Questa˜o 4P(X > 3 |X > 1) = P(X > 3)P(X > 1) = 1− P(X ≤ 3)1− P(X ≤ 1)
P(X < 3) = 12 · 3 · f (3) = 1, 5 · 0, 08 · 3 = 0, 36
P(X < 1) = 12 · 1 · f (1) = 0, 5 · 0, 08 · 1 = 0, 04
P(X > 3 |X > 1) = 1− P(X ≤ 3)1− P(X ≤ 1) = 1− 0, 361− 0, 04 = 0, 6667
Questa˜o 5
P(X > c) = 0, 6 ⇒ P(X ≤ c) = 0, 4 ⇒ 12 · c · f (c) = 0, 4 ⇒c · 0, 08c = 0, 8⇒ c2 = 10⇒ c = ±√10Soluc¸a˜o: c = √10 ≈ 3, 1623
Questa˜o 6
Questa˜o 7
f (x) = 120 = 0, 05 90 ≤ x ≤ 110
AD1 – MEstII – 1/2018 2
Questa˜o 8 P(X > 105) = 0, 05 · (110− 105) = 0, 25
Questa˜o 9 P(X < 92) = 0, 05 · (92− 90) = 0, 10
Questa˜o 10
(110− c) · 0, 05 = 0, 95⇒ 110− c = 19⇒ c = 91
Questa˜o 11
P(Z > 2, 1) = 0, 5− tab(2, 1) = 0, 5− 0, 4821 = 0, 0179
Questa˜o 12
P(Z < 1, 83) = 0, 5 + tab(1, 83) = 0, 5 + 0, 4664 = 0, 9664
Questa˜o 13
P(−2, 24 < Z < −1, 50) = P(1, 50 < Z < 2, 24) =tab(2, 24)− tab(1, 50) = 0, 4875− 0, 4332 = 0, 0543
Questa˜o 14
P(−2, 33 < Z < 1, 96) = tab(2, 33)+tab(1, 96) = 0, 4901+0, 475 =0, 9651
AD1 – MEstII – 1/2018 3
Questa˜o 15
P(1, 8 < Z < 2, 4) = tab(2, 4) − tab(1, 8) = 0, 4918 − 0, 4641 =0, 0277
Questa˜o 16
P(Z > k) = 0, 01⇒ tab(k) = 0, 49⇒ k = 2, 33
Questa˜o 17
P(Z < k) = 0, 02 ⇒ P(Z > −k) = 0, 02 ⇒ tab(−k) = 0, 48 ⇒−k = 2, 05⇒ k = −2, 05
Questa˜o 18
P(Z > k) = 0, 9 ⇒ P(Z < k) = 0, 1 ⇒ P(Z > −k) = 0, 1 ⇒tab(−k) = 0, 4⇒ k = −1, 28
Questa˜o 19
P(|Z | > k) = 0, 05⇒ tab(k) = 0, 475⇒ k = 1, 96
Questa˜o 20
P(|Z | ≤ k) = 0, 90⇒ tab(k) = 0, 45⇒k = 1, 64 ou 1, 65 ou 1, 645
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