mean # of strokes/hole is 3.3 variance and standard deviation using Poisson distri?

Question

mean number of strokes per hole is 3.3

What is the variance?

What is the standard deviation?
 

How likely is the golfer to play 18 hole round and have more than 72 strokes?

Answer 1

Variance=mean=3.3, SD=sqrt(3.3)=1.82 approx.

Poisson probability P(X)=(e^-µ)µ^X/X!, where µ=mean.

P(72/18)=P(4)=e^-3.3*3.3^4/4!=0.182 is the probability of averaging 72 in 18 holes.

Exclude P(0) in this case because it has no meaning to average zero strokes per hole.

Probability of more than 4 strokes per hole is (1-probability of 1, 2, 3 or 4 strokes per hole).

Probability of more than 4 strokes per hole is 1-(P(1)+P(2)+P(3)+P(4))=

1-e^-3.3(3.3+3.3^2/2+3.3^3/6+3.3^4/24)=

1-3.3e^-3.3(1+3.3/2+3.3^2/6+3.3^3/24)=0.2743 or 27.43%.