Question

According to a consumer survey of young adults​ (18-24 years of​ age) who shop​ online, 23​% own a mobile phone with internet access. In a random sample of 300 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, dependent​ trials, where there are only two possible​ outcomes, S​ (for Success) and F​ (for Failure).

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 varies from trial to trial. The variable x is the number of​ F'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 remains the same from trial to trial. The variable x is the number of​ S's in n trials.

b. What is the value of​ p? Interpret this value. p equals nothing ​(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 is

npnp.

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

C.For any young​ adult, the probability that they do not 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 1 minus p1−p.

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

​E(x)equals=nothing

Choose the correct interpretation below.

A.In a random sample of 300 young adults Upper E left parenthesis x right parenthesis 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 300 young adults Upper E left parenthesis x right parenthesisE(x) will always be the number of young people surveyed that will own mobile phones with internet access.

C.In a random sample of 300 young adults Upper E left parenthesis x right parenthesis E(x) is the largest possible number of young people surveyed that will own mobile phones with internet access.

D.In a random sample of 300 young adult Upper E left parenthesis x right parenthesis E(x)

is the average number of young people surveyed that will own mobile phones with internet access.

Click to select your answer(s).

need asap thanks

Answer 1

a) Option (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 remains the same from trial to trial. The variable x is the number of​ S's in n trials.

b) p = 0.23, Option (B)

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

c)

​E(x) = np = 300 * 0.23

= 69

Option (D)

In a random sample of 300 young adult Upper E left parenthesis x right parenthesis E(x) is the average number of young people surveyed that will own mobile phones with internet access.