In each of the following cases, 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 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.
(e) A basketball players makes three quarters of his free throw attempts. Assume that all of his free throw attempts are independent. A player takes 300 free throw attempts in year.
X = the number of free throw attempts made.