Question

As the assistant bank manager, you want to provide prompt service for customers at your bank's drive thru window. The bank can currently serve up to 10 customers per 15-minute period without significant delay. The average arrival rate is 7 customers per 15-minute period. Let x denote the number of customers arriving per 15-minute period. Assume this is a Poisson distribution.

a. Find the probability that 10 customers will arrive in a
particular 15-minute period.

b. Find the probability that 10 or fewer customers will arrive in a
particular 15-minute period.

c. Does your bank have prompt service? Are there ways that your
bank can improve their customer service? How?

Answer #1

Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 30 customers
per hour or 0.5 customers per minute. In the same bank waiting line
system, assume that the service times for the drive-up teller
follow an exponential probability distribution with a service rate
of 36 customers per hour, or 0.6...

Problem 15-3 (Algorithmic) Willow Brook National Bank operates a
drive-up teller window that allows customers to complete bank
transactions without getting out of their cars. On weekday
mornings, arrivals to the drive-up teller window occur at random,
with an arrival rate of 18 customers per hour or 0.3 customers per
minute. In the same bank waiting line system, assume that the
service times for the drive-up teller follow an exponential
probability distribution with a service rate of 30 customers per...

A grocery store counts the number of customers who arrive during
an hour. The average over a year is 20 customers per hour. Assume
the arrival of customers follows a Poisson distribution. (It
usually does.)
Find the probability that at least one customer arrives in a
particular one minute period. Round your answer to 3
decimals.
Find the probability that at least two customers arrive in a
particular 4 minute period. Round your answer to four decimals.

Let average number of customers arriving at a bank is 40/hour.
Find the probability that exactly 6 customers will arrive at the
bank during a 15 minute period.

Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 24 customers
per hour or 0.4 customers per minute. Also assume that the service
times for the drive-up teller follow an exponential probability
distribution with a service rate of 36 customers per hour, or 0.6
customers per minute. Determine the probabilities...

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...

The National Bank of Germany is opening a new bank teller.
Management estimates that customers will arrive at the rate of 10
per hour. The teller who will staff the window can serve customers
at the rate of one every four minutes.
Assuming Poisson arrivals and exponential service, find:
Average number of customers in the system.
Average time in the system.
Average waiting time in the line.
Average number of customers in the line.
Utilization of the teller.

Problem 11-04 (Algorithmic)
Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 24 customers
per hour or 0.4 customers per minute. Also assume that the service
times for the drive-up teller follow an exponential probability
distribution with a service rate of 36 customers per hour, or 0.6
customers per minute....

1. Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 6 customers
per hour or 0.1 customers per minute. Also assume that the service
times for the drive-up teller follow an exponential probability
distribution with a service rate of 54 customers per hour, or 0.9
customers per minute. Determine the...

An automatic roller coaster ride takes a constant time of 2.5
minutes to complete a ride. Customers arrive at the facility every
2.75 minutes (exponentially distributed). Report answers to 4
decimal places.
a. Determine the average waiting time in the queue (in
minutes).
b. The local bank drive-through teller window can serve a
customer at an average of 4.5 minutes per customer (exponentially
distributed). Customers arrive in their cars at a rate of 12 per
hour (poisson distributed). Determine the...

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