solution

 

. A “hit” for a Web site is a request for a file from the Web site’s server computer. Some popular Web sites have thousands of hits per minute. One popular Web site boasts an average of 6500 hits per minute between the hours of 9 A.M. and 6 P.M. Some weaker software packages will have trouble calculating Poisson probabilities with such a large value of μ.

(a) Try calculating the probability of 6400 or more hits during the minute beginning at 10:05 A.M. using the software that you

have available. Did you get an answer? If not, how did the software respond?

(b) Now, use the central limit theorem to calculate the probability of 6400 or more hits during the minute beginning at 10:05 A.M.

To do this, think of the number of hits in this minute as the sum of the number of hits for each of the 60 seconds in this minute. We can express P(sum of hits for each of the 60 seconds ≥ 6400) as P(x ≥ 6400/60) where x is the average number of hits per

second for the 60 seconds in the minute of interest.