Question

According to a consumer survey of young adults​ (18-24 years of​ age) who shop​ online, 29​% 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, with more than two possible outcomes. The probability that an event occurs varies from trial to trial.

B.

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.

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, dependent​ trials, where there are only two possible​ outcomes, S​ (for Success) and F​ (for Failure).

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 own a mobile phone with internet access is1−p.

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

C.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 not own mobile phones with internet access.

B.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.

C.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.

D.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.

Answer 1