According to a consumer survey of young adults (18-24 years of age) who shop onl
ID: 3200883 • Letter: A
Question
According to a consumer survey of young adults (18-24 years of age) who shop online, 34% own a mobile phone with internet access. In a random sample of 200 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, 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. 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, 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 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 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 np.
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.
E(x)=
Choose the correct interpretation below.
A. In a random sample of 200 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 200 young adults E(x) will always be the number of young people surveyed that will own mobile phones with internet access.
C. In a random sample of 200 young adults E(x) is the average number of young people surveyed that will own mobile phones with internet access.
D. In a random sample of 200 young adults E(x) is the largest possible number of young people surveyed that will own mobile phones with internet access.
Click to select your answer(s).
Explanation / Answer
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, 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.
A. For any young adult, the probability that they own a mobile phone with internet access is p.
p = 0.34
c. What is the expected value of x? Interpret this value.
E(x)= n*p
= 200*0.34
= 68
C. In a random sample of 200 young adults E(x) is the average number of young people surveyed that will own mobile phones with internet access.