Question

A certain tennis player makes a successful first serve 70% of the time. Assume that each

serve is independent of the others. If she serves 7 times, answer the following questions.

a. Verify the distribution of X, the number of first serves in. (Check the binomial conditions.)

b. What is the mean number of first serves in?

c. Find the probability that she gets at least 5 first serves in.

Answer 1

a) As each serve made is independent of the other serves, and the probability of successful serve made is equal for each of the serve trial. Also there is a fixed number of served made that is 7 here. Therefore the distribution here is a binomial distribution given as:

b) The mean number of first serves is computed here as:

Mean = np = 7*0.7 = 4.9

Therefore, 4.9 is the mean number of first serves in here.

c) The probabiltiy that she gets at least 5 first serves in is computed here as:

= P(X = 5) + P(X = 6) + P(X = 7)

Therefore 0.6471 is the required probability here.