Question

The average number of customers arriving at a bank branch is eight per hour. Assume that customer arrivals follow a Poisson process. The bank opens at 9:00 am in the morning. Answer the following questions accordingly.

a) What is the probability that the first customer will arrive after 9:10 am?

b) Suppose that it is now 9:15 and the first customer has arrived at 9:12 am. What is the probability that the second customer will arrive after 9:25 am?

c) What is the probability that the third customer arrives exactly at 9:45 am?

d) What is the probability that exactly three customers arrive by 9:45 am?

Answer #1

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.

Suppose that customers arrive at a bank at a rate of 10 per
hour. Assume that the number of customer arrivals X follows a
Poisson distribution.
Find the probability of more than 25 people arriving within the
next two hours using the Poisson mass function.
Find the probability of more than 25 people arriving within the
next two hours using the normal approximation to the Poisson.
Compute the percent relative difference between the exact
probability computed in part 1 and...

Suppose that customers arrive at a bank at a rate of 10 per
hour. Assume that the number of customer arrivals X follows a
Poisson distribution.
1. Find the probability of more than 25 people arriving within
the next two hours using the Poisson mass function.
2. Find the probability of more than 25 people arriving within
the next two hours using the normal approximation to the
Poisson.
3. Compute the percent relative difference between the exact
probability computed in...

Individual customers arrive at a coffee shop after it opens at 6
AM. The number of customers arriving by 7AM has a Poisson
distribution with parameter λ = 10. 25% of the customers buy a
single donut and coffee, and 75% just buy coffee. Each customer
acts independently. Answer the following:
a.What are the two random variables described above and what are
their probability
mass functions?
b.What is the probability that exactly five customers arrive by
7AM?
c.If 10 customers...

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 grocery store at an average of 2.2 per
minute. Assume that the number of arrivals in a minute follows the
Poisson distribution. Provide answers to the following to 3 decimal
places.
What is the probability that at least seven customers arrive in
three minutes, given that exactly two arrive in the first
minute?

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...

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.

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...

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?

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