Question: The average score for male golfers is 95 and the average score for female golfers is 106. Use these values as the population means for men and women and assume that the population standard deviation is \(\sigma \) =14 strokes for both. A simple random sample of 30 male golfers and another random sample of 45 female golfers will be taken.

a. Show the sampling distribution of x for male golfers.

b. What is the probability that the sample mean is within three strokes of the population mean for the sample male golfers?

c. What is the probability that the sample mean is within three strokes of the population mean for the sample female golfers?

d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within three strokes of the population mean higher? Why?