Question

. For each of the following questions, say whether the random process is reasonably a binomial process or not, and explain your answer. As part of your explanation, you will want to comment on the potential validity of each of things that must be true for a process to be a binomial process. If it is a binomial process, identify n : the number of Bernoulli trials and π the probability of success.

(a) A fair die is rolled until a 1 appears, and X denotes the number of rolls.

(b) Ten different basketball players each attempt 1 free throw and X is the total number of successful attempts.

(c) It has been reported that nation-wide, one-third of all credit card users pay their bills in full each month. Let X be the number of people in a sample of 25 randomly chosen credit card users in Madison who pay their bill in full on a given month.

(d) Let X be the number of months out of a randomly chosen year that one randomly chosen credit card user in Madison pays their bill in full.

Answer 1

(a)

The random process is not a binomial distribution since = probability of success in each trial is not constant.

(b)

The random process is a binomial distribution.

n = the number of Bernoulli trials = 10

= the probability of success = 1/10 = 0.1

(c)

The random process is a binomial distribution.

n = the number of Bernoulli trials = 25

= the probability of success = 1/3 = 0.3333

(d)

The random process is not a binomial distribution since = probability of success in each trial is not constant.