1) Exactly 100 employees of a firm have each purchased one ticket in a lottery, with the drawing to be held at the firm's annual party. Of 80 men who purchased a ticket, 25 are single. Only 4 of the women who purchased a ticket are single.

(a) draw a probability table for this situation.

(b) If the winner is single, what is the probability that she is a woman?

(c) If the winner is married, what is the probability that he is a man?

2)The percentage of undergraduate students in the United States receiving federal financial aid is 40%. Consider a random sample of 25 such students. Let X be the number of students in the sample who receive financial aid.

(a) Calculate the mean and the standard deviation of X

(b) What is the probability that in the random sample of 25 students at least 13 students receive financial aid?

(c) What is the probability that in the random sample of 25 students less than 10 students receive financial aid?

3) A university must decide between two health plans for its faculty and stuff. An impor1 tant piece of information in making this decision is the average annual medical expenses of the individual employees. A random sample of 20 employees was surveyed. In this group the average annual medical expense was $1,782. The sample standard deviation is s = $560.

(a) Construct a 95% confidence interval for the true average medical expense of the university employees. Assume that the population distribution is normal

(b) Construct a 99% confidence interval for the true average medical expense of the university employees