In each of the following situations, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case. If a binomial distribution applies, give the values of n and p.

(a) A poll of 200 college students asks whether or not you usually feel irritable in the morning. X is the number who reply that they do usually feel irritable in the morning.

Yes, a binomial distribution is reasonable; B(200, 1/2).

Yes, a binomial distribution is reasonable; B(p, 200).

Yes, a binomial distribution is reasonable; B(200, p).

Yes, a binomial distribution is reasonable; B(1/2, 200).

No, a binomial distribution is not reasonable.

(b) You toss a fair coin until a head appears. X is the count of the number of tosses that you make.

Yes, a binomial distribution is reasonable; B(X, p).

Yes, a binomial distribution is reasonable; B(1/2, n).

Yes, a binomial distribution is reasonable; B(n, 1/2).

Yes, a binomial distribution is reasonable; B(n, p).

No, a binomial distribution is not reasonable.

(c) Most calls made at random by sample surveys don't succeed in talking with a person. Of calls to New York City, only one-twelfth succeed. A survey calls 500 randomly selected numbers in New York City. X is the number of times that a person is reached.

Yes, a binomial distribution is reasonable; B(500, 1/2).

Yes, a binomial distribution is reasonable; B(1/12, 500).

Yes, a binomial distribution is reasonable; B(1/2, 500).

Yes, a binomial distribution is reasonable; B(500, 1/12).

No, a binomial distribution is not reasonable.

(d) You deal 10 cards from a shuffled deck of standard playing cards and count the number X of black cards.

Yes, a binomial distribution is reasonable; B(10, 1/2).

Yes, a binomial distribution is reasonable; B(1/4, 10).

Yes, a binomial distribution is reasonable; B(1/2, 10).

Yes, a binomial distribution is reasonable; B(10, 1/4).

No, a binomial distribution is not reasonable.

. With n = 175 and P = .34, find the probability (X = 50) using the binomial distribution and the normal approximation to the binomial distribution if the conditions for normal approximation to the binomial distribution are met. . With n = 175 and P = .34, find the probability (X