For which of the following is a binomial distribution appropriate for the variable X?
a) When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random dialing machine make 15 calls. X is the number that reach a live person.
(b) A couple really wants to have a boy. They decide that they will keep having children until they have their first boy. Successive births are independent and each has about probability 0.5 of being a boy or a girl. X is the number of the pregnancy that finally succeeds at bringing a baby boy to the couple.
(c) A manufacturer of medical catheters randomly selects 8 catheters, one from each hours production for a detailed quality inspection. One variable recorded is the count X of catheters with an unacceptable diameter (too small or too large).
(d) A sample survey asks 10 people randomly selected from a family of 50 people whether they oppose the legalization of medical marijuana. X is the number of persons who say Yes.
(e) Niacin is particularly important for men over 50 since it helps them to maintain healthy blood cholesterol levels. A researcher randomly selects 10 men over 50 years old and records whether or not each individual's level of niacin in his bloodstream is high, average, or low. X is the number of men with high niacin.
(f) A nurse instructs an adult patient to take his resting pulse 10 times over the next few days. A resting pulse requires resting for at least 10 minutes before taking the pulse. X is the number of measurements that are below 100 beats per minute.