A company is preparing to launch a new web site to sell its products. From past

Question

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

a) What is the expected time in minutes before the first purchase after the site opens? Give your answer to four decimal places. 1

b) What is the probability that more than 0.23 minutes pass before the first purchase? Give your answer to four decimal places. 2

c) What is the expected time in minutes until the sixth purchase? Give your answer to four decimal places. 3

d) 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. 4

Explanation / Answer

Solution:-

a) 1/(22/10) = 10/22 = 0.4545

b) e^-rt = e^-22/10(.23) = e^-0.506 = 0.6029

c)  1/(22/10) * 6 = 60/22 = 2.7273

d)  P(12.27 <t(4th purchase)<3.18) = 1 - (0.6170+0.6988) = 0.3158

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