Question

In a recent​ year, the mean number of strokes per hole for a famous golfer was approximately 3.3.  How likely is this golfer to play an​ 18-hole round and have more than 72​ strokes?

Answer 1

 

72 strokes for 18 holes is a mean of 4 strokes per hole.

If we use Poisson with µ=3.3 then Po(X,µ)=µ^Xe^-µ/X! is the probability of exactly X strokes per hole.

To find out Po(X>4,µ) we need to work out these probabilities for X in [0,4] and subtract the resultant sum from 1. Although it is not possible to have a hole in no strokes, we nevertheless need to include the probability because Poisson is being used as a model.

For X between 0 and 4 we have:

Po(0,3.3)=0.03688

Po(1,3.3)=0.12171

Po(2,3.3)=0.20083

Po(3,3.3)=0.22091

Po(4,3.3)=0.18225

Sum=0.7626 approx

Therefore 1-0.7626=0.2374 or 23.74%.