Question

The number of hits to a website follows a Poisson process. Hits occur at the rate of 1.8 per minute between​ 7:00 P.M. and 9​:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 7 : 43 P.M. and 7​:48 P.M.

Interpret each result.

​(a) exactly eight ​(

b) fewer than eight ​

(c) at least eight ​

(a)​ P(8​) =______ ​(Round to four decimal places as​ needed.)

(b) P (fewer than 8) = _______​(Round to four decimal places as​ needed.)

(c) P (at least 8) = _______​(Round to four decimal places as​ needed.)

Answer 1

First we calculate hit rate between 7:43 .P.M and 7:48 P.M. ( 5 minutes )

Given hit rate = 1.8 per minute

In five minutes, hit rate = 1.8 x 5 = 9 hits

Using the above formula, we calculate the following probabilities;

a)

There is 13.18% chance that exactly 8 hits between 7:43 .P.M and 7:48 P.M.

b)

= 0.3239

There is 32.39% chance that less than 8 hits between 7:43 .P.M and 7:48 P.M.

c)

= 0.6761

There is 67.61% chance that at least 8 hits between 7:43 .P.M and 7:48 P.M.