The average score of all golfers for a particular course has a mean of 61 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the
49 golfers exceeded 62.
A).4772
B).0228
C).1293
D).3707

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, we can calculate the probability that the average score of 49 golfers exceeded 62. The standard error (SE) of the mean is the standard deviation divided by the square root of the sample size, which is 3.5 / sqrt(49) = 0.5. We then calculate the z-score for a mean of 62, which is (62 - 61) / 0.5 = 2. The probability of a z-score exceeding 2 is approximately 0.0228, using standard normal distribution tables or a calculator.

The Average Score of All Golfers for a Particular Course