Question

According to a consumer survey of young adults​ (18-24 years of​ age) who shop​ online, 30% own a mobile phone with internet access. In a random sample of 400 young adults who shop​online, let x be the number who own a mobile phone with internet access.

a. Explain why x is a binomial random variable​ (to a reasonable degree of​ approximation). Choose the correct explanation below.

A. The experiment consists of n​ identical, dependent​ trials, where there are only two possible​ outcomes, S​ (for Success) and F​ (for Failure).

B.The experiment consists of n​ identical, dependent​ trials, with more than two possible outcomes. The probability that an event occurs varies from trial to trial.

C. The experiment consists of n​ identical, independent​ trials, where there are only two possible​ outcomes, S​ (for Success) and F​ (for Failure). The probability of S remains the same from trial to trial. The variable x is the number of​ S's in n trials.

D.The experiment consists of n​ identical, independent​ trials, where there are only two possible​ outcomes, S​ (for Success) and F​ (for Failure). The probability of S varies from trial to trial. The variable x is the number of​ F's in n trials.

b. What is the value of​ p? Interpret this value.

p=______________________​(Type an integer or a​ decimal.)

Choose the correct interpretation of p below.

A. For any young​ adult, the probability that they do not own a mobile phone with internet access is p.

B.For any young​ adult, the probability that they own a mobile phone with internet access is 1 minus p1−p.

C.For any young​ adult, the probability that they own a mobile phone with internet access is p.

D.For any young​ adult, the probability that they own a mobile phone with internet access is np

c. What is the expected value of​ x? Interpret this value.

​E(x)=_______________Choose the correct interpretation below.

A.In a random sample of 400 young adults E(x) is the average number of young people surveyed that will own mobile phones with internet access.

B.In a random sample of 400 young adults E(x) is the largest possible number of young people surveyed that will own mobile phones with internet access.

C.In a random sample of 400 young adults E(x) is the average number of young people surveyed that will not own mobile phones with internet access.

D.In a random sample of 400 young adults E(x) will always be the number of young people surveyed that will own mobile phones with internet access.

Answer 1

Given that x is a binomial random variable

for binomial distribution all trails should be independent and identical

there should be 2 possibilities either success or failure

Answer 2

ANSWER :

1. Option C 

2. p = 0.30 . Option C 

3. E(x) = n p = 400 * 0.30 = 120 ; Option A.