5. A male golfer has an average score of 95 and a female a 106 (Golf Digest, April 2006). Consider these values as the population means for men and women and assume that the population standard deviation is = 14 strokes in both cases. A simple random sample of 40 male golfers and another of 45 female golfers will be taken.

to. Give the sampling distribution of for male golfers.

b. What is the probability that, in the case of male golfers, the sample mean does not differ by

more than 3 strokes from the population mean?

c. What is the probability that, in the case of female golfers, the sample mean does not differ by

more than 3 strokes from the population mean?

d. In which of the cases, part a or part b, is the probability that the sample mean does not differ

in more than 3 strokes of the population mean? Why?