Question

8. Assume that the number of student complaints that arrive at dean's office can be modeled as a Poisson random variable. Also assume that on the average there are 5 calls per hour. a) What is the probability that there are exactly 8 complaints in one hour? b) What is the probability that there are 3 or fewer complaints in one hour? c) What is the probability that there are exactly 12 complaints in two hours? d) What is the probability that there are exactly 4 complaints in 30 minutes?

Answer 1

8)

X =poisson with lambda = 5/hour

a) for one hour

$\lambda$ = 5

P(X =8)

=e^(-5) * 5^8 /8!

= 0.065278

b)

P(X <= 3)

= P(X =0) + P(X = 1) + P(X = 2) + P(X = 3)

= 0.26503

c)

for two hours

$\lambda$ = 5*2 = 10

P(X = 12) =

0.09478

d)

for 30 minutes

$\lambda$ = 5/2 = 2.5

P(X =4) = 0.1336