Question

The number of customers arriving per hour at a certain automobile service facility is
assumed to follow a Poisson distribution with mean λ = 6.
(a) Compute the probability that more than 20 customers will arrive in a 3-hour period.
(b) What is the probability that the number of customers arriving in a 2-hour period will
not exceed 40?
(c) What is the mean number of arrivals during a 4-hour period?

Answer 1

Let Nt = # to customers driving during time interval of the length t.

Nt ~ Poission(lambda. time)

lambda= 6

a)

t = 3

lambda = 6*3 = 18

P (N3 > 20) = 1 - P(N3 <= 20) = 1 -F(20)

= 1- 0.95209

= 0.04791

b)

lambda = 2 *6 = 12

P(N2<=40) = F(40)

= 1

c)

E(N4) = lambda * t

= 6 * 4

= 24