A company is preparing to launch the new web site to sell its products. From past experience, they know that purchases at the site will take place as a Poisson process with on average 25 purchases every ten minutes.
a. Determine the expected time in minutes before the first purchase after the site opens? Provide your answer to four decimal places.
b. Compute the probability that more than 0.15 minutes pass before the first purchase? Give your answer to four decimal places.
c. Calculate the expected time in minutes until the fifth purchase? Give your answer to four decimal places.
d. Find out the probability that the fifth purchase will occur between 1.6 minutes and 2.4 minutes after the site opens? Give your answer to four decimal places.