Assignment:
The average score for male golfers is 95 and the average score for female golfers is 106 (Golf Digest, April 2006). Use these values as the population means for men and women and assume that the population standard deviation s = 14 strokes for both. A simple random sample of 30 male golfers and another simple random sample of 45 female golfers will be taken.
a. Show the sampling distribution of x for male and female golfers.
b. What is the probability that the sample mean is within 3 strokes of the populations mean for the sample of male golfers?
c. What is the probability that the sample mean is within 3 strokes of the populations mean for the sample of female golfers?
d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 3 strokes of the population mean higher? Why?
Provide complete and step by step solution for the question and show calculations and use formulas.