Question

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 get the answer.)

B.What is the probability that the time to service is 2 minutes or less? (again – formulas with numbers plugged in should be included with your answer to show your work.)

C.What is the probability that the time to service is more than 2 minutes (formulas with numbers plugged in should be shown as well as the answer.)

D.What is the probability that exactly 5 customers show up in 5 minutes?

E.What is the probability that at least one customer shows up in 5 minutes?

Answer #1

**Answer:**

Given,

Service Rate = 0.6 customers per minute

Hence, Mean Time to Service =

**Solution-A:**

Let the time to service is denoted by variable that has exponential distribution

Probability that time to service is 1 minute or less:

**Solution-B:**

Probability that time to service is 2 minute or less:

**Solution-C:**

Probability that time to service time is more than 2 minutes =

**Solution-D:**

on average there will be 0.6*5=3 customes in 5 minutes

P(x=5)=e^{-3}*(3^5/5!)=**0.1008**

**Solution-E:**

P(x >= 1) = 1 - P(x = 0 ; 3) = 1 - e^{-3} = 1 -
0.0498 = **0.9502**

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 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....

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...

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...

A Security Pacific Bank branch has opened up a drive through
teller window. There is a single service lane, and customers in
their cars line up in a single line to complete bank transactions.
The average time for each transaction to go through the teller
window is exactly four minutes. Throughout the day, customers
arrive independently and largely at random at an average rate of
ten customers per hour.
What is the probability that a customer gets to complete his/her...

Scenario: There is only one teller working at a bank. The teller
takes an average of 3 minutes to service a customer. Assume that
the time the teller takes to service a customer can be represented
as an Exponential Probability distribution.
Customers arrive at the teller line at the average rate of 1every
10 minutes. Their arrival pattern follows a Poisson
distribution.
Of 200 customers who get serviced by the teller, how many can
expect to be serviced in more...

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...

Customers arrive at bank according to a Poisson process with
rate 20 customers per hour. The bank lobby has enough space for 10
customers. When the lobby is full, an arriving customers goes to
another branch and is lost. The bank manager assigns one teller to
customer service as long as the number of customers in the lobby is
3 or less. She assigns two tellers if the number is more than 3 but
less than 8. Otherwise she assigns...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 17 minutes ago

asked 17 minutes ago

asked 19 minutes ago

asked 24 minutes ago

asked 27 minutes ago

asked 38 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago