According to a consumer survey of young adults (18-24 years of age) who shop onl

Question

According to a consumer survey of young adults (18-24 years of age) who shop online, 26% 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, 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, dependent trials, where there are only two possible outcomes, S (for Success) and F (for Failure).

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=___ 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 own a mobile phone with internet access is 1 minus p1p.

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

c. What is the expected value of x? Interpret this value. Choose the correct interpretation below. E(x)= _____

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

B. In a random sample of 300 young adults E (x) is the average number of young people surveyed that will not own mobile phones with internet access.

C. In a random sample of 300 young adults 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 adults E(x) is the average number of young people surveyed that will own mobile phones with internet access.

Explanation / Answer

a) Correct Answer: 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) Correct Answer: Option (B) For any young adult, the probability that they own a mobile phone with internet access is p.

c) Correct Answer: Option (D) In a random sample of 300 young adults E(x) is the average number of young people surveyed that will own mobile phones with internet access.

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