Approximately 300 million golf balls were lost in the United

Approximately 300 million golf balls were lost in the United States in 2009. Assume that the number of golf balls lost in an 18-hole round is distributed as a Poisson random variable with a mean of 5 balls.

a. What assumptions need to be made so that the number of golf balls lost in an 18-hole round is distributed as a Poisson random variable?

Making assumptions given in (a), what is the probability that...

b. 0 golf balls will be lost in an 18-hole round?

c. 5 or fewer balls will be lost in an 18-hole round?

d. 6 or more balls will be lost in an 18-hole round?

Solution

(a)

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(b) Given X~Poisson(mean=5)

P(X=x)=5^x*exp(-5)/x!

So the probability is

P(X=0) = 5^0*exp(-5)/1 = 0.006737947

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(c) P(X<=5) = P(X=0)+P(X=1)+...+P(X=5)

= 5^0*exp(-5)/1 + 5^1*exp(-5)/1+....+ 5^5*exp(-5)/5!

=0.6159607

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(d) P(X>=6) =1-P(X<=5)

=1-0.6159607

=0.3840393