Question

According to a consumer survey of young adults​ (18-24 years of​age) who shop​ online, 33​% own a mobile phone with internet access. In a random sample of 500 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. pequals=?(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 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 npnp. 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 500 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. B. In a random sample of 500 young adults Upper E left parenthesis x right parenthesisE(x) is the average number of young people surveyed that will own mobile phones with internet access. C. In a random sample of 500 young adults Upper E left parenthesis x right parenthesisE(x) is the largest possible number of young people surveyed that will own mobile phones with internet access. D. In a random sample 500 young adults Upper E left parenthesis x right parenthesisE(x) is the average number of young people surveyed that will not own mobile phones with internet access.

Answer 1

Answer:

a. 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.

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

c. A. In a random sample of 500 young adults Upper E left parenthesis x right parenthesis E(x) will always be the number of young people surveyed that will own mobile phones with internet access.

Explanation:

A binomial random variable is mostly used to show the number of successful results in a repeated number of binomial experiments. Thus, we can infer that the variable 'x' has the properties of a binomial random variable. The expected value of the variable 'x' is equivalent to the probability-weighted mean of all possible values of x.