A golf tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13th 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. Sixty-four golfers played the hole with the new placement on that day. Required:
Determine the probability of the sample average number of strokes exceeding 4.75 using the historical mean and standard deviation.