Question

In a large department store a customer-complaints office handles an average of six complaints per hour about the quality of service. The distribution is Poisson.

A. What is the probability that in any hour exactly six complaints will be received? Please show in Excel too.

B. What is the probability that more than 20 minutes will elapse between successive complaints? Please show in Excel too.

C. What is the probability that fewer than 5 minutes will elapse between successive complaints? Please show in Excel too.

D. The store manager observes the complaints office for a 30-minute period, during which no com- plaints are received. He concludes that a talk he gave to his staff on the theme “the customer is always right” has obviously had a beneficial effect. Suppose that, in fact, the talk had no effect. What is the probability of the manager observing the office for a period of 30 minutes or longer with no complaints? Please show in Excel too.

Answer 1

a) Poisson DistributionP(x) = e^−λ λ^x ∕ x!

Mean = 6
Number of events = 6
Cumulative = False

=POISSON.DIST(6,6,False)

There is a .1606

b)
Exponential Distribution X = 20
Lambda = 1/6
Cumulative = True
P(T > 20) =1-EXPON.DIST(20,(1/6),TRUE)
= 0.0357
There is a .0357

c)
Exponential DistributionX = 5
Lambda = 1/6
Cumulative = True
P(T < 5)=EXPON.DIST(5,(1/6),TRUE) = P( T < 5 )
= 0.5654
There is a .5654

d)
Exponential Distribution X = 30
Lambda = 1/6
Cumulative = True
P(T > 30)=1-EXPON.DIST(30,(1/6),TRUE)
= 0.00674
There is a .00674