Question

A store lets customers enter one at a time. Suppose that the entries follow a Poisson process with a mean of 10 customers per hour. (a) What is the probability that exactly 11 customers enter in a given hour?

(b) What is the probability that exactly 18 customers enter in a given two-hour period?

(c) A new greeter starts their shift at noon. What is the probability that they let their first customer enter before 12:15?

Answer #1

A restaurant opens at 10:00AM and customers come in according to
a Poisson process with an average of 3 customers per hour.
(a) What is the probability the fourth customer will come in
before noon?
(b) What is the probability the second customer will come in
between 9:00AM and 11:30AM?

The number of customers that enter a Starbucks follows a Poisson
distribution with an average of 2 customers every 15 minutes.
(a) What is the probability that on the next hour at least six
customers enter this Starbucks?
(b) Assuming that a customer just walked in, what is the
probability that the next customer walks in after 15 minutes?
(c) Suppose 5% of people who pass this Starbucks enter for a
coffee. What are the chances that among the next...

Thirty percent (30%) of all customers who enter a store will
make a purchase. Suppose that 6 customers enter the store and that
these customers make independent purchase decisions. Let x be the
number of the 6 customers who will make a purchase.
Use the binomial formula to calculate
The probability that exactly 2 customers make a purchase.
The probability that 2 or fewer customers make a purchase.
The probability that at least 1 customer makes a purchase

The number of customers that enter a bank follows a Poisson
distribution with an average of 30 customers per hour. What is the
probability that exactly 3 customers would arrive during a 12
minute period?
Select one:
a. 0.4211
b. 0.1008
c. 0.2586
d. 0.1404
e. 0.0892

A store typically has 5 customers arrive per hour, and arrivals
follow a Poisson distribution. What is the likelihood that a. no
customers will arrive in an hour? b. less than three customers
arrive in an hour? c. five or more customers arrive in an hour?

Suppose the time a student takes on an exam can be modeled by a
Poisson process with a mean of 20 questions per hour Let X denote
the number of questions completed.
A)What is the probability of a student finishing exactly 18
questions in the next hour?
B)What is the probability of a student finishing
exactly 12 questions in 30 minutes?
C) What is the probability of finishing at
least 1 question in the next minute?

Suppose the time a student takes on an exam can be modeled by a
Poisson process with a mean of 20 questions per hour Let X denote
the number of questions completed.
A)What is the probability of a student finishing
exactly 18 questions in the next hour?
B)What is the probability of a student finishing
exactly 12 questions in 30 minutes?
C) What is the probability of finishing at
least 1 question in the next minute?

Customers are arriving to a shop according to Poisson process
with mean 2.7 customers/hour. What is the probability that the next
customer will arrive after 23 minutes but before 38 minutes?

1. Suppose the expected number of customers entering a
department store between 9 AM and 10 AM is 60.
a. What is the probability that exactly 1 customer enters
between 9:00 and 9:01 ?
b. What is the probability that exactly 2 customers enter
between 9:00 and 9:02 ?
c. What is the probability that exactly 2 customers enter
between 9:00 and 9:01 GIVEN THAT exactly two customers enter
between 9:00 and 9:02?

Suppose that the number of customers ordering take-out at a
small restaurant is a Poisson process with rate α = 4.0 customers
per hour.
Answer the following questions. If necessary, round your answer to
four decimal places.
(a) Find the probability that there would be at least two
customers in a 450-minute period.
(b) The cashier in charge of take-outs wishes to take a 35 -
minute break starting right after serving a customer. What is the
probability that there...

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