Question

The number of hits to a Web site follows a Poisson process. Hits occur at the rate of 1.2 per minute between 7pm and 12 pm. Given below are three scenarios for the number of hits to the Website. Compute the probabilityof each scenario between 8:21pm and 8:24pm.

a. exactly six

b. fewer than six

c. at least six

Answer 1

Let X = Number of hits between 8:21pm and 8:24pm.

The rate of hits between 8:21pm and 8:24pm. is 1.2*3 = 3.6

Therefore X follows Poisson distribution with parameter = 3.6

a) P ( exactly six hits between 8:21pm and 8:24pm) = P( X = 3)

Using excel:

P( X = 6) = "=POISSON(6,3.6,0)" = 0.082608

b) P ( Fewer than six hits between 8:21pm and 8:24pm) = P( X < 6) = P( X <= 5)

P( X <= 5) = "=POISSON(5,3.6,1)" = 0.844119

P(   At least six hits between 8:21pm and 8:24pm ) = P(X >= 6) 0.155881

P(X >= 6) = 1- P( X < 6) = 1 - 0.844119 = 0.155881