A company is preparing to launch a new web site to sell its products. They know that purchases at the site will occur as a Poisson process with on average 22 purchases every 10 minutes.

Question

What is the expected time in minutes until the sixth purchase? Give your answer to four decimal places.  

(ANS: 2.7273)

What is the probability that the sixth purchase will occur between 2.27 minutes and 3.18 minutes after the site opens? Give your answer to four decimal places.  

Answer 1

6/(22/10) = 60/22 = 30/11 = 2 8/11 = 2.7273

P(sixth purchase between 2.27 and 3.18 minutes) = P(5 or less purchases in 2.27 minutes) - P(5 or less purchases in 3.18 minutes) = P(X <= 5; λ = 2.27 * 22/10) - P(X <= 5; λ = 3.18 * 22/10)

Your calculator may be able to give you this. In Excel, poisson.dist(5,2.27*22/10,1) - poisson.dist(5,3.18*22/10,1) = .3158