The number of jobs sent to a printer follows a Poisson distr

The number of jobs sent to a printer follows a Poisson distribution with a mean of 4 per hour.
A. What is the probability that exactly 4 jobs send to the printer in one hour?
B. What is the probability that the printer receives 6 jobs in 2 hours?
C. What is the probability that more than 1 jobs are received in period of 20 minutes.
D. Let T be the waiting time, in hours, between jobs.
i. What is the mean waiting times?
ii. Find P(,25 < T < .5)
iii. What is the probability that the next job is sent within 15 minutes.

Solution

Mean =4

Let X : no of jobs sent to the printer in 1 hour.

a) P(X=4) = 0.1954

b) P(X=3) = 0.1954(for 2 hours 6 mean one hour 3)

c) P(X>3) = 0.5665

d)

i) Mean waiting time = 1/4 = 15 minutes

ii) P(0.25

iii) P(T<15) = P(X>4) = 0.3712