Question

The number of hits to a Web site follows a Poisson process. Hits occur at the rate of 0.8 per minute between​ 7:00 P.M. and 11​: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 : 39 P.M. and 8​:48 P.M. and interpret the results.

​(a) exactly seven hits ​

(b) fewer than seven hits

​(c) at least seven hits

Answer 1

Hits occur = 0.8 per minute

Time between 8: 39 PM and 8 48 PM, there are 10 m inutes.

Expected number of hits in 10 minutes = 10 * 0.8 = 8

(a) So here if x is the number of hits in 10 minutes between 8: 39 PM and 8: 48 PM

then x ~ POISSON (8)

p(x) = e^-8 8^x/x!

so here we have to find

P(Exactly seven hits) = e^-8 8⁷/7! = 0.1396

that means the probability to get exactly 7 calls in between 8: 39 PM and 8: 48 PM is 0.1396.

(b) P(x < 7) =

it will be calculated by using poisson distribution formula from EXCEL

P(x < 7) = POISSON (6; 8 ; TRUE) = 0.3134

that means the probability to have less than 7 calls in between 8: 39 PM and 8: 48 PM is 0.3134

(c) P(x 7) =1 - P(x < 7) = 1 - 0.3134 = 0.6866

that means the probability to have more than 7 calls in between 8: 39 PM and 8: 48 PM is 0.6866.