Atividade - Statistics 3

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 Pergunta 1 
1 em 1 pontos 
 
 The probability table below summarizes the information that a large cable company provides about its 
customers: 
 
 
Where: 
T is the event that a randomly chosen customer subscribes to TV service 
I is the event that a randomly chosen customer subscribes to Internet service 
 
 
Create a probability table to organize and summarize information and use it 
to find probabilities 
"multiple choice" question: select the correct answer. 
What is the probability that a randomly chosen customer subscribes to 
exactly one of the two services? 
 
 
Resposta Selecionada: 
.15 
Resposta Correta: 
.15 
Feedback da resposta: This is correct. 
 
 
 Pergunta 2 
1 em 1 pontos 
 
 An epidemiological study reported the following information about two contagious diseases: 
· There is 15% chance of contracting Disease I 
· There is 20% chance of contracting Disease II 
· There is 2% chance of contracting both diseases 
Let A be the event that a randomly chosen person contracts Disease I 
Let B be the event that a randomly chosen person contracts Disease II 
Apply probability rules in order to find the likelihood of an event 
"multiple choice" question: select the correct answer. 
What does the probability P(A or B) mean in this context? 
 
 
Resposta 
Selecionada: 
 
The probability of contracting at least one of the two 
diseases 
Resposta Correta: 
The probability of contracting at least one of the two 
diseases 
Feedback da 
resposta: 
This is correct. P(A or B) is the probability of contracting 
Disease I or Disease II or both. In other words, P(A or B) is the 
probability of contracting at lease one of the two diseases. 
 
 
 Pergunta 3 
1 em 1 pontos 
 
 A family eats out twice a month – once during the first week of the month and once during the third 
week of the month, in one of the three local restaurants: R1, R2, or R3. Thus the outcome (R3, R2) 
denotes that on a given month the family eats in R3 during the first week of the month and in R2 
during the third week of the month. It is possible for the family to eat at the same restaurant both on 
the first week and on the third week of the month. 
 
 
Apply probability rules in order to find the likelihood of an event 
"multiple choice" question: select the correct answer. 
Let event A and event B be two disjoint events. Which of the following is 
incorrect? 
 
 
Resposta Selecionada: 
Event A is the complement of Event B. 
Resposta Correta: 
Event A is the complement of Event B. 
Feedback da resposta: This is correct. This is the only incorrect statement. 
 
 
 Pergunta 4 
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. 
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 
Selecionada: 
 
The mean of the sampling distribution will stay the same, but the standard 
deviation will increase. 
 
Resposta Correta: 
The mean of the sampling distribution will stay the same, but the standard 
deviation will increase. 
Feedback da resposta: This is correct. 
 
 Pergunta 5 
1 em 1 pontos 
 
 The following three probability histograms represent the probability distributions of the random 
variables X, Y, and W. 
As is evident from the probability histograms, the mean of all three random variables is 5. 
 
 
 
Find the mean and variance of a discrete random variable, and apply these 
concepts for solving real world problems. 
 
"multiple choice" question: select the correct answer. 
Which of the three random variables has the largest standard deviation? 
 
Resposta Selecionada: 
X 
Resposta Correta: 
X 
Feedback da resposta: This is correct. 
 
 
 Pergunta 6 
1 em 1 pontos 
 
 The probability table below summarizes the information that a large cable company provides about its 
customers: 
 
 
Where: 
T is the event that a randomly chosen customer subscribes to TV service 
I is the event that a randomly chosen customer subscribes to Internet service 
 
 
Create a probability table to organize and summarize information and use it 
to find probabilities 
"multiple choice" question: select the correct answer. 
What is the correct representation and probability of the event that a 
customer subscribes only to TV service? 
 
 
Resposta Selecionada: 
P(T and Not I) = .05 
Resposta Correta: 
P(T and Not I) = .05 
Feedback da resposta: This is correct. 
 
 
 Pergunta 7 
1 em 1 pontos 
 
 Understand how probability quantifies uncertainty and relate the 
probability of an event to the likelihood of the event occurring. 
"multiple choice" question: select the correct answer. 
Let A be the event that a document will reach its destination on time using 
a certain service. If P(A)=.98 
this means that: 
 
 
Resposta 
Selecionada: 
 
The document will almost always reach its destination on 
time 
Resposta Correta: 
The document will almost always reach its destination on 
time 
Feedback da resposta: This is correct. 
 
 
 Pergunta 8 
0 em 1 pontos 
 
 An epidemiological study investigated the prevalence of two contagious 
diseases ( Disease 1 and Disease 2) in the U.S. 
Let A be the event that an individual contracts Disease 1 
Let B be the event that an individual contracts Disease 2 
Determine whether two events are independent 
"multiple choice" question: select the correct answer. 
Recall that the epidemiological study reported the following: 
· There is 15% chance of contracting Disease 1 (Event A) 
· There is 10% chance of contracting Disease 2 (Event B) 
· There is 3% chance of contracting both Disease 1 and Disease 2 
Are the two diseases being contracted independently of each other (are 
events A, B independent)? 
 
 
Resposta 
Selecionada: 
 
Yes, since P(A and B) > 0 
 
Resposta Correta: 
No, since P(A and B)=.03 is not equal to 
P(A)*P(B)=.15*.10=.015 
 
 Pergunta 9 
0 em 1 pontos 
 
 The National Survey on Drug and Health reported that 15% females in the 
age group of 12 to 20 years old are binge drinkers. 
A random sample of 10 females from this age group is chosen, and let the 
random variable X be the number of females (out of 10) who are binge 
drinkers. 
Fit the binomial model when appropriate, and use it to perform probability 
calculations. 
"multiple choice" question: select the correct answer. 
Which of the following is the correct probability distribution function of 
X? 
 
 
Resposta 
Selecionada: 
 
P(X=x)=10!x!(10−x)! ⋅ 0.15x ⋅ 0.8510−x x=1, 2, 3...9, 
10 
Resposta Correta: 
P(X=x)=10!x!(10−x)! ⋅ 0.15x ⋅ 0.8510−x x=0, 1, 2, 3...9, 10 
 
 
 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. 
In which of the following scenarios we cannot safely assume that the sampling distribution of the 
sample mean X¯¯¯ is normal or approximately normal? 
 
Resposta 
Selecionada: 
 
The weight of the baggage checked by an individual passenger has mean 
μ=50pounds and standard deviation σ=15 pounds. A random sample of n=10 
passengers is selected and the average weight of their checked baggage, x¯, is 
determined. 
Resposta 
Correta: 
 
The weight of the baggage checked by an individual passenger has mean 
μ=50pounds and standard deviation σ=15 pounds. A random sample of n=10 
passengers is selected and the averageweight of their checked baggage, x¯, is 
determined. 
 
Feedback da 
resposta: 
This is correct. We can assume that the sampling distribution of the sample mean is 
normal (or approximately normal) as long as at least one of the following two 
conditions holds: 
• the variable of interest (weight in this case) is known to have a 
normal distribution in the population 
• the sample size is large enough (n>30) 
• In other words, the only case when we cannot assume that the sampling distribution 
of the sample mean is normal is when neither of the two conditions holds.In this 
case, we are not told that weights have anormal distribution and n=10<30. 
 
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