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?
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
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