1. A PGA (Professional Golf Association) tournament organizer is attempting to d

Question

1. 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 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 2 strokes, and the distribution is assumed normal. 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 that the sample average number of strokes is greater than 4.50.

Explanation / Answer

Here, mean = 4.25 , s = 2 , n =64

By central limit theorem,

P(x > 4.50)

z = ( x - mean) / ( s/sqrt(n))

= ( 4.50 - 4.25) / ( 2/sqrt(64))

= 1

we need to find P( z > 1)

P(x > 4.500 = p( z > 1) = 0.1587

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