Find the probability of between 5 and 7 email messages received (endpoints included) in a given minute.

Question

Records show that the average number of email messages received per minute is 7.7. Find the probability of between 5 and 7 email messages received (endpoints included) in a given minute.

Round answer to 4 decimal places.

Answer 1

Poisson lambda = 7.7

Prob ( X = k) = lambda^k / { exp(lambda) * k! }

Excel says:

That exp(lambda) =

k Lambda^k k! Prob(X=k)

5 27067.84 120 0.102142

6 208422.4 750 0.131082

7 1604852 5040 0.144191

For a total of 0.377415

So 37.7415%