Avaliação - Statistics 3 v2

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Pergunta 1 
1 em 1 pontos 
 
This is correct. This is the only incorrect statement. 
A 2015 CNN Money article provided the following information about the social class 
distribution of U.S. adults. 
 
Apply probability rules in order to find the likelihood of an event 
"multiple choice" question: select the correct answer. 
Two U.S. adults are chosen at random. What is the probability that both adults 
belong to the same social class? 
 
 
Resposta Selecionada: 
.29 * .29 + .50 * .50 + .21 * .21 
Resposta Correta: 
.29 * .29 + .50 * .50 + .21 * .21 
Feedback 
da 
resposta: 
This is correct. P(Both belong to the same social class) = P(Both 
Lower class or Both Middle class or Both Upper class) = 
[disjoint]P(Both Lower class) + P(Both Middle class) + P(Both 
Upper class) = [independence].29 * .29 + .50 * .50 + .21 * .21 
 
 
Pergunta 2 
1 em 1 pontos 
 
Skill: Determine the sampling distribution of the sample proportion and the sample 
mean in a given situation and apply it to determine likelihoods. 
"multiple choice" question: select the correct answer. 
A random sample of 21 credit card users is chosen.What is the mean and standard 
deviation of pˆ, the sample proportion of credit card users who pay their bill in full 
every month? (some answers are rounded). 
 
Resposta Selecionada: 
Mean = 0.30, standard deviation = 0.1 
Resposta Correta: 
Mean = 0.30, standard deviation = 0.1 
 
Feedback da 
resposta: 
This is correct. The mean is the population proportion p = 0.30 and 
the standard deviation is p(1−p)n−−−−−√=.3(1−.3)21−−−−−−√=0.1 
 
Pergunta 3 
1 em 1 pontos 
 
Fit the binomial model when appropriate, and use it to perform probability 
calculations. 
"multiple choice" question: select the correct answer. 
The National Survey on Drug Use and Health also reported that 21% of males 
in the same age group (12-20) are binge drinkers. 
Suppose that in addition to the 10 randomly chosen females, a random sample 
10 males from the same age group is chosen (to a total of 20). 
Let the random variable Y be the total number of males and females (out of 20) 
who are binge drinkers. 
Which of the following is true regarding the random variable Y? 
 
Resposta Selecionada: 
Y has a binomial distribution with n=20 and p=.18 
Resposta Correta: 
Y has a binomial distribution with n=20 and p=.18 
Feedback da 
resposta: 
This is correct. p=0.15 for 10 of the trials (the 10 females) 
and p=0.21 for the other 10 trials (the 10 males). 
 
 
Pergunta 4 
0 em 1 pontos 
 
A lot of research is conducted on the sleeping habits of U.S. adults. One study 
reported that X, the amount of sleep per night of U.S. adults follows a normal 
distribution with mean μ=7.5 hours and standard deviation σ=1.2 hours. 
 
P(8.5<X≤9.5) 
Find probabilities associated with the normal distribution. 
"multiple choice" question: select the correct answer. 
 
Using the Standard Deviation Rule, what is the probability that a randomly 
chosen U.S. adult sleeps more than 8.7 hours per night? 
 
Resposta Correta: 
0.16 
 
 
Pergunta 5 
0 em 1 pontos 
 Fit the binomial model when appropriate, and use it to perform probability 
calculations. 
"multiple choice" question: select the correct answer. 
What are the mean and standard deviation of X, the number of females out of 
the 10 chosen who are binge drinkers? 
 
 
Resposta Correta: 
μx=10(0.15) , σx=10(0.15)(0.85)−−−−−−−−−−−−√ 
 
 
Pergunta 6 
0 em 1 pontos 
 
Skill: Determine the sampling distribution of the sample proportion and the sample 
mean in a given situation and apply it to determine likelihoods. 
"multiple choice" question: select the correct answer. 
It was reported that 30% of all credit card users in the U.S. pay their card card bill in 
full every month.A random sample of size n=84 credit cards users is chosen. Which 
of the following is true regarding the effect of the increased sample size (from 21 to 
84) on the mean and standard deviation of sampling distribution of pˆ? 
 
Resposta 
Correta: 
 
The mean of the sampling distribution will stay the same, but the 
standard deviation will increase. 
 
 
Pergunta 7 
1 em 1 pontos 
 
Skill: Determine the sampling distribution of the sample proportion and the sample 
mean in a given situation and apply it to determine likelihoods. 
"multiple choice" question: select the correct answer. 
Scores of the Math portion of the SAT (SAT-M) are known to have a national mean 
μ=500and standard deviation σ=100. 
A random sample of n=400 high-school seniors was chosen and their average SAT-M 
score was found to be x̅=522. 
Would this finding surprise you? 
 
Resposta 
Selecionada: 
 
Yes, since an average of 522 is more than 4 standard 
deviations above 500. 
Resposta Correta: 
Yes, since an average of 522 is more than 4 standard 
deviations above 500. 
Feedback 
da 
resposta: 
This is correct. The mean and standard deviations of the sampling 
distribution of x-bar are μ=500and σn√=100400√=5, repectively. x-
bar = 522 is therefore more than 4 standard deviations above 500 [to 
be precise (522-500)/5=4.4 standard deviations above 500]. We 
know that getting a value that is more than 4 standard deviations 
above the mean in a normal distribution is very unusual and therefore 
x-bar=522 is a surprising result. 
 
 
Pergunta 8 
1 em 1 pontos 
 
Skill: Determine the sampling distribution of the sample proportion and the sample 
mean in a given situation and apply it to determine likelihoods. 
"multiple choice" question: select the correct answer. 
What is the mean and standard deviation of the sampling distribution of x¯, the 
average number of defects in a sample of size n=225? 
 
Resposta Selecionada: 
Mean = 3.6, standard deviation = 0.5 
Resposta Correta: 
Mean = 3.6, standard deviation = 0.5 
Feedback da 
resposta: 
This is correct. The mean and standard deviations are 
μ=3.6 and σn√=7.5225√=0.5, repectively. 
 
 
Pergunta 9 
0 em 1 pontos 
 Airlines sometimes overbook flights. Suppose that for a plane with 111 seats an 
airline takes 115 reservations. Let the random variable X be the number of 
people who actually show up (out of the 115 who bought a ticket). From past 
experience the probability distribution of X is given in the following table: 
x 108 109 110 111 112 113 114 115 
P(X=x) 0.14 0.16 0.24 0.20 0.13 0.06 0.05 0.02 
 
 
Resposta Selecionada: 
0.20 
Resposta Correta: 
0.74 
 
 
Pergunta 10 
1 em 1 pontos 
 
Skill: Determine the sampling distribution of the sample proportion and the sample 
mean in a given situation and apply it to determine likelihoods. 
"multiple choice" question: select the correct answer. Suppose that the average 
number of defects in the sample of n=225cars was found to be x̅=5.1. What is the z-
score of this average? 
 
 
Resposta Selecionada: 
3 
Resposta Correta: 
3 
Feedback da resposta: This is correct. Z=x¯ −μσn√=5.1−3.67.5225√=1.50.5=3