A PGA (Professional Golf Association)tournament organizer is attempting to determine whether hole (pin)placement has a significant impact on the average number of strokes for the 13^th hole on a given golf course.Historically,the pin has been placed in the front right corner of the green,and the historical mean number of strokes for the hole has been 4.25,with a standard deviation of 1.6 strokes.On a particular day during the most recent golf tournament,the organizer placed the hole (pin)in the back left corner of the green.64 golfers played the hole with the new placement on that day.Determine the probability of the sample average number of strokes exceeding 4.75. A).9938 B).4013 C).0062 D).3783

Question

Quizplus · Accepted Answer

We are given:
Historical mean number of strokes = μ1 = 4.25
Standard deviation = σ = 1.6 
Sample size = n = 64
New mean number of strokes = μ2 = ?
We can use the central limit theorem to approximate the sampling distribution of the sample mean. Since the sample size is large enough, we can assume that the sampling distribution follows a normal distribution with mean μ2 and standard error (σ/√n).
To find the new mean, we can use the fact that the sample average is an unbiased estimator of the population mean. Therefore, we can assume that the sample average is equal to μ2, and we can use it to estimate the probability of the sample average exceeding 4.75 strokes.
z = (X̄ - μ) / (σ / √n)
z = (4.75 - 4.25) / (1.6 / √64)
z = 2.5
Using a standard normal distribution table, we can find the probability of z being greater than 2.5. The probability is:
P(z > 2.5) = 0.0062
Therefore, the answer is C) 0.0062.

A PGA (Professional Golf Association)tournament Organizer Is Attempting to Determine