How to find the probability of the sample average number of strokes exceeding 4.75.
A PGA (Professional Golf Association) tournament organizer is trying to determine whether hole (pin) placement has an important impact on the average number of strokes for the 13th hole on a given golf course and 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 utmost recent golf tournament and the organizer placed the whole (pin) in the back left corner of the green. 64 golfers played the fleabag with the new placement on that day. Conclude the probability of the ex average number of strokes exceeding 4.75.