Question

Please solve using **EXCEL** and show steps.

In the Northwest Bank waiting line system, assume that the service times for drive-up teller follow an exponential probability distribution with a mean of 100 customers per hour. Use the exponential probability distribution to answer the following questions:

a. What is the probability that the service time is one minute or less?

b. What is the probability that the service time is two minutes or less?

c. What is the probability that the service time is more than two minutes?

d. What is the probability that the service time is between three and seven minutes?

Need to interpret the results for these problems; if you are unsure of the direction the question asks (left tail, right tail, etc.), draw a diagram.

Answer #1

Exponential/Poisson
Megacity Bank operates a drive-up teller window that
allows customers to complete bank transactions without having to
get out of their car. Megacity Bank waiting line times follow an
exponential distribution with a service rate of 36 customers per
hour.
A.What is the probability that the time to service is 1 minute
or less? (show your formula with the numbers plugged in, as well as
the answer. You may use the e^(-λ) table, an advanced calculator or
excel to...

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...

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...

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...

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...

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....

A fast-food franchise is considering operating a drive-up window
food-service operation. Assume that customer arrivals follow a
Poisson probability distribution, with an arrival rate of 25 cars
per hour, and that service times follow an exponential probability
distribution. Arriving customers place orders at an intercom
station at the back of the parking lot and then drive to the
service window to pay for and receive their orders. The following
service alternative is being considered:
System C: A two-server operation with...

A fast-food franchise is considering operating a drive-up window
food-service operation. Assume that customer arrivals follow a
Poisson probability distribution, with an arrival rate of 24 cars
per hour, and that service times follow an exponential probability
distribution. Arriving customers place orders at an intercom
station at the back of the parking lot and then drive to the
service window to pay for and receive their orders. The following
three service alternatives are being considered:
System A: A single-server operation...

Question 2
A fast-food franchise is considering
operating a drive-up window food-service operation. Assume that
customer arrivals follow a Poisson probability distribution, with
an arrival rate of 24 cars per hour, and that service times follow
an exponential probability distribution. Arriving customers place
orders at an intercom station at the back of the parking lot and
then drive to the service window to pay for and receive their
orders. The following three service alternatives are being
considered:
A single-channel operation...

The bank manager wants to show that the new system reduces
typical customer waiting times to less than 6 minutes. One way to
do this is to demonstrate that the mean of the population of all
customer waiting times is less than 6. Letting this mean be
µ, in this exercise we wish to investigate whether the
sample of 93 waiting times provides evidence to support the claim
that µ is less than 6.
For the sake of argument, we...

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