Question

At ABC Bank, customers arrive at a teller line at a rate of 10 per five-minute period. Assuming that customers arrive randomly and independently, use the Poisson probability distribution to answer the following questions: (8 points)

a.What is the probability that no customers arrive in a five-minute period?

b.What is the probability that 3 or fewer customers arrive in a five-minute period?

c.What is the probability that no customers arrive in a one-minute period?

d.What is the probability that at least 1 customer arrives in a one-minute period?

Answer 1

Poisson probability distribution Formula = P(x; ?) = (e^-?) (?^x) / x!

x = Number of Happenings

a. Probability that no customers arrive in a five minute period

F(0) = 10^0 e^-10 / 0! = e^-10 = 0.00045

f(0) = 0.00045 from Poisson Probability table

b. the probability that 3 or few customers arrive in a five-minute period

From the Poisson probability table with ?= 10,

P(X?3)= f(0)+f(1)+f(2)+f(3) = 0+0.0005+0.0023+0.0076 = 0.0104

c. the probability that no customers arrive in a one-minute period

Number of customers in a 2 minute period = ? =10/5 = 2

f(0) = 0.1353 from the Poisson probability table on with ?= 2 and x=0

d. the probability that at least 1 customer arrive in a one-minute period

From c, f(0) = 0.1353

P(at least one customer = 1-f(0) = 1-0.1353 = 0.8647