Question

Look at the following cases and determine whether the variable of interest has a binomial distribution. If it does, give the values of the parameters N and P. If it doesn't, explain why not.
A. You are dealt a five-card poker hand. X = the number of Diamonds in your hand.
B. You randomly select one card from each of ten different decks of playing cards. X = number of Clubs selected.
C. Heights of females in some population follow a normal distribution with a mean of 65 inches and standard deviation of 1.5 inches. We take a random sample of three women. X = number of women in the sample shorter than 64 inches.
D. A boy asks the same girl to go out on a date every day for a week. X = the number of times the girl agrees to go on the date.
E. A multiple choice exam has 30 questions with choices (A, B, C, D and E). An unprepared student guess all of the answers. X = the number of answers he gets correct.

Answer 1

A distribution is binomial when their is only two available choices for the variable of interest.

In option A, X is not a binomial distribution because there are more than two diamonds in a card.

In option B, X is not a binomial distribution because there are more than two clubs in a card.

In option C, X is a binomial distribution because a woman in the sample can either be shorter than 64 inches or not.

In option D, X is a binomial distribution because a girl in the sample can either agree to a date or not.

In option E, X is a binomial distribution because a student in the sample can either be shorter than 64 inches or not.