Question

Customers arrive at a restaurant according to a Poisson distribution at a rate of 30 customers per hour. The restaurant opens for business at 11:00 am. (Assume that customers will stay long enough). Find the probability of having 20 customers in the restaurant at 11:12 am given that there were 17 customers at 11:07 am.

Answer #1

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?

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?

Customers arrive to a savings bank according to a Poisson
distribution with mean 3 per hour. Then, they either complete a
transaction with a bank teller or meet with a financial officer,
and leave the bank when they are done.
What is the probability that exactly 2 customers arrive in the
next three hours?
What is the probability that at least 3 customers arrive in the
next two hours?
What is the probability that nobody arrives in the next 30...

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.

At an airport domestic flight arrive according to a Poisson
distribution with rate 5 per hour, and international flights arrive
according to a Poisson distribution with rate 1 per hour. What is
the probability that the time between third and fourth flight
arrivals is more than 15 minutes?

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.

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 nail salon according to a poisson process
with rate 10 per hour. 30% of customers come in for only a
manicure. 30% only for a pedicure, and 40% for both.
what is the expe ted waiting time in MINUTES between manicure
oy customer arrivals?

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)...

4. Suppose that customers arrive at a bank according to a P P(λ)
with λ = 12 per hour. Compute the following: (a) The mean and
variance of the customers who enter the bank during 5 hours. (b)
Probability that more than 5 customers enter the bank during an
hour. (c) Probability that exactly 1 arrival between 9:00am and
11:00am and exactly 2 arrivals between 10:00am and 12:00 noon.

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