Question

**ANSWER THE FOUR PARTS OR DON'T ANSWER AT
ALL.**

- Mixed Poisson/exponential

Customers arrive at the drive-up window of a fast-food restaurant at a rate of 2 per minute during the lunch hour (12-1pm).

a. What is the probability that exactly 3 customers will arrive in 1 minute? 1 customer will arrive in 5 minutes?

b. What is the probability that no customers will arrive in 2 minutes?

c. Given a customer has just arrived, what is the probability that the next customer will arrive within 1 minute? 2 minutes?

d. Given a customer has just arrived, what is the probability the next customer will NOT arrive within the next 2 minutes?

Answer #1

a)P( exactly 3 customers will arrive in 1 minute
)=e^{-2}*2^{3}/3! =0.180447

P( 1 customer will arrive in 5 minutes
)=e^{-2*5}*(5*2)^{1}/1! =0.000454

b) probability that no customers will arrive in 2 minutes
=P(X=0)=e^{-2*2}*(2*2)^{0}/0! =0.018316

c)

probability that the next customer will arrive within 1 minute
=1-P(X=0)=1-e^{-2}*2^{0}/0! =0.864665

probability that the next customer will arrive within 2 minute
=1-P(X=0)=1-e^{-2*2}*(2*2)^{0}/0! =0.981684

d)

probability the next customer will NOT arrive within the next 2
minutes = e^{-2*2}*(2*2)^{0}/0! =0.018316

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...

B. Customers arrive at a restaurant according to a Poisson
process. On the average, a customer arrives every half hour.
(a) What is the probability that, 1 hour after opening, there at
least one customer has arrived?
(b) What is the probability that at least 2 customers have
arrived?

Customers arrive at a bank according to a Poisson process with
rate 10 per hour.
Given that two customers arrived in the ﬁrst 5 minutes, what is
the probability that
(a) both arrived in the ﬁrst 2 minutes.
(b) at least one arrived in the ﬁrst 2 minutes.

Starting at noon, diners arrive at a restaurant according to a
Poisson process at
the rate of five customers per minute. The time each customer
spends eating at
the restaurant has an exponential distribution with mean 40
minutes, independent
of other customers and independent of arrival times. Find the
distribution,
as well as the mean and variance, of the number of diners in the
restaurant at
2 p.m.

Customers arrive at a shop at the rate of 7 per 10-minute
interval. what is the probability that we need to wait at least 10
minutes before the next customer arrives at the shop? Obtain the
probability using Poisson distribution and Exponential
distribution.

An exponential probability distribution has lambda equal to 21
customers per hour. Find the following probabilities.
a) What is the probability that the next customer will arrive
within the next 3 minutes?
b) What is the probability that the next customer will arrive
within the next 15 seconds?
c) What is the probability that the next customer will arrive
within the next 12 minutes?
d) What is the probability that the next customer will arrive
within the next 17 minutes?

Let X = the time between two successive arrivals at the drive-up
window of a local bank. If X has an exponential distribution with λ
= 1/3 , compute the following:
a. If no one comes to the drive-up window in the next 15 minutes
(starting now), what is the chance that no one will show up during
the next 20 minutes (starting now)?
b. Find the probability that two people arrive in the next
minute.
c. How many people...

Customers arrive to the checkout counter of a convenience store
according to a Poisson process at a rate of two per minute. Find
the mean, variance, and the probability density function of the
waiting time between the opening of the counter and the following
events:
A) What is the probability that the third customer arrives
within 6 minutes? You can use a computer if you’d like but you need
to write down the integral with all of the numbers plugged...

At the Fidelity Credit Union, a mean of 44 customers arrive
hourly at the drive-through window. What is the probability that,
in any hour, less than 11 customer will arrive? Round your answer
to four decimal places.

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago