Question: On Monday mornings, the First National Bank only has one teller window open
for deposits and withdrawals. Experience has shown that the average number of
arriving customers in a 4-minute interval on Monday mornings is 2.8, and each
teller can serve more than that number efficiently. These random arrivals at
this bank on Monday mornings are Poisson distributed.
a. What is the probability that on a Monday morning exactly six customers will
arrive in a 4-minute interval?
b. What is the probability that no one will arrive at the bank to make a
deposit or withdrawal during a 4-minute interval?
c. Suppose the teller can serve no more than four customers in any 4-minute
interval at this window on a Monday morning. What is the probability that
during any given 4-minute interval, the teller will be unable to meet the
demand? What is the probability that the teller will be able to meet the
demand? When demand cannot be met during any given interval, a second window is
opened. What percentage of the time will a second window have to be opened?
d. What is the probability that exactly three people will arrive at the bank
during a 2-minute period on Monday mornings to make a deposit or a withdrawal?
What is the probability that five or more customers will arrive during an 8-
minute period?