Fans arriving on a given Saturday night for a nonconference

Fans arriving on a given Saturday night for a non-conference home basketball game average 0.33 per second. Let x represents the number of fans arriving at a specified time period. What is the probability that from 13 to 15 fans arrive between 7:15 and 7:16 P.M.? (Round your answer(s) to 3 decimal places.)

Solution

Given X follows Poisson distribution with mean=0.33*60=19.8 per minutes

P(X=x)=(19.8^x)*exp(-19.8)/x! for x=0,1,2,...

So the probability is

P(13<=X<=15) = P(X=13)+P(X=14)+P(X=15)

=(19.8^13)*exp(-19.8)/13!+(19.8^14)*exp(-19.8)/14!+(19.8^15)*exp(-19.8)/15!

=0.124