A small town has 100 people in it. 45 of them are men and 55 are women. It is also known that there are 48 Democrats in the town and 52 Republicans. We do not know how many of the women are Republicans or Democrats, or how many of the men are Republicans or Democrats, however. We are interested in the number of female Republicans. Assume thatwomen and men are both equally likely to be a Democrat or a Republican.
(a) What is the probability that there are exactly 5 female Republicans?
(b) What is the probability that there are 25 female Republicans?
(c) What is the expected number of female Republicans?
(d) What is the variance and standard deviation of the number of female Republicans?