Question

The number of hits to a Web site follows a Poisson process. Hits occur at the rate of 0.9 per minute between​ 7:00 P.M. and 10​:00

P.M. Given below are three scenarios for the number of hits to the Web site. Compute the probability of each scenario between 8:12 P.M.

and 8​:21 P.M.

​(a) exactly four.

​(b) fewer than four.

​(c) at least four.

Answer 1

Given Hits occur at the rate of 0.9 per minute

Between 8:12 P.M and 8​:21 P.M we have 9 minutes

λ = 0.9 * 9 = 8.1

​(a) exactly four

P(X = K) = (e^-λ * λ^k)/k!

P(X = 4) = (e^-8.1 * 8.1^4)/4! = 0.05444

​(b) fewer than four.

P(X = K) = (e^-λ * λ^k)/k!

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) +P(X = 3) = 0.03961

or Excel : POISSON.DIST(3,8.1,TRUE) = 0.039605

​(c) at least four

P(X >= 4) = 1 - P(X < 4) = 1-0.03961 = 0.96039