ATIVIDADE 3 STATISTCS

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· Pergunta 1
1 em 1 pontos
	
	
	
	A large cable company provides the following information regarding its customers:
· 50% of all customers subscribe to internet service.
· If a customer is an internet subscriber, there is 64% chance that he/she is also a phone subscriber.
· If a customer is a phone subscriber, there is 80% chance that he/she is also an internet subscriber.
Let A be the event that a customer subscribes to internet service
Let B be the event that a customer subscribes to phone service
Use the general multiplication rule to find P(A and B)
"multiple choice" question: select the correct answer.
What is the probability that a customer subscribes to both internet and phone service?
	
	
	
	
		Resposta Selecionada:
	 
P(A) * P(B|A) = .50 * .64 = .32
	Resposta Correta:
	 
P(A) * P(B|A) = .50 * .64 = .32
	Feedback da resposta:
	This is correct. P(A and B) = P(A) * P(B|A) = .50 * .64 = .32
	
	
	
· Pergunta 2
1 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
Understand the reasoning behind the concept of conditional probability, calculate conditional probabilities and interpret them.
"multiple choice" question: select the correct answer.
Below is the probability table for the two contagious diseases example.
A is the event that an individual contracts Disease 1
B is the event that an individual contracts Disease 2
The fraction .12/.90 represents:
	
	
	
	
		Resposta Selecionada:
	 
P(A | Not B)
	Resposta Correta:
	 
P(A | Not B)
	Feedback da resposta:
	This is correct. P(A | Not B)=P(A and Not B)/P(Not B)=.12/.90
	
	
	
· Pergunta 3
1 em 1 pontos
	
	
	
	The weekly cost of maintenance and repairs for a company has a normal distribution with mean μ=$5500 and standard deviation σ=$400.
Note: For questions 19 and 20 you will need to use the Normal Table linked here
Find probabilities associated with the normal distribution.
"multiple choice" question: select the correct answer.
How much should be budgeted for weekly maintenance and repair so that there is only 1.5% chance that the cost will exceed the budgeted amount.
	
	
	
	
		Resposta Selecionada:
	 
6368
	Resposta Correta:
	 
6368
	Feedback da resposta:
	This is correct. Working with the table inside out (looking for the closest table’s entry to .985) we find that the z-score of the value we are looking for is z=2.17
The required budgeted amount is therefore: 5500 + 2.17(400) = 6368.
	
	
	
· Pergunta 4
1 em 1 pontos
	
	
	
	Find the mean and variance of a linear transformation of a random variable, and the mean and variance of the sum of two independent random variables.
"multiple choice" question: select the correct answer.
Based on accumulated data, a propane gas company determined that the random variable X, the number of gallon required to fill a customer’s propane tank, has mean μx=300 gallons and standard deviation σx=40 gallons. The company charges the customer $25 service fee plus $2.50 per gallon of propone.
What is the mean and standard deviation of the amount that a customer is billed for?
	
	
	
	
		Resposta Selecionada:
	 
mean = $775, standard deviation = $100
	Resposta Correta:
	 
mean = $775, standard deviation = $100
	Feedback da resposta:
	This is correct.
	
	
	
· Pergunta 5
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 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.
In context, the fact that P(Not T and Not I) = 0 means that:
	
	
	
	
		Resposta Selecionada:
	 
All the customers subscribe to at least one of the two services.
	Resposta Correta:
	 
All the customers subscribe to at least one of the two services.
	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
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.
20% of all the students at a large university are international students. Two random samples of students are chosen; a random sample of n=64 students and a random sample of n=400 students. In which of the two samples is it more likely that more than 25% of the sampled students are international students?
	
	
	
	
		Resposta Selecionada:
	 
The sample of size n=64 since in there is more variability in the proportion of international students in smaller samples.
	Resposta Correta:
	 
The sample of size n=64 since in there is more variability in the proportion of international students in smaller samples.
	Feedback da resposta:
	This is correct.
	
	
	
· Pergunta 9
1 em 1 pontos
	
	
	
	The weekly cost of maintenance and repairs for a company has a normal distribution with mean μ=$5500 and standard deviation σ=$400.
Note: For questions 19 and 20 you will need to use the Normal Table linked here
Find probabilities associated with the normal distribution.
"multiple choice" question: select the correct answer.
If $6200 is budgeted for the next week, what is the probability that the cost will exceed the budgeted amount?
	
	
	
	
		Resposta Selecionada:
	 
.0401
	Resposta Correta:
	 
.0401
	Feedback da resposta:
	This is correct.
P(X>6200)=[z=6200−5500400=1.75]=P(Z>1.75)=[table]=1−.9599=0401
	
	
	
· Pergunta 10
1 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.
Find probabilities associated with the normal distribution.
"multiple choice" question: select the correct answer.
Using the Standard Deviation Rule, 2.5% of U.S. adults sleep less than how many hours per night?
	
	
	
	
		Resposta Selecionada:
	 
5.1
	Resposta Correta:
	 
5.1
	Feedback da resposta:
	This is correct. By the Standard deviation Rule 95% of U.S. adults sleep between 7.5 – 2(1.2) = 5.1 hours and 7.5 + 2(1.2)=9.9 hours. Therefore, 2.5% of U.S. adults sleep less than 5.1 hours.