Question

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?

Answer #1

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.

suppose starting at 8am buses arrive at a bus stop according to
the poisson process at a rate of one every 15 mins. if the 1st bus
has not arrived by 815am what is the probability it will arrive
before 830 am.
B. find the probability that the 3rd bus arrives after 9am. note
we do not assume the condition that the 1st bus has not arrived by
815 am as stated above

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 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...

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.

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.

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...

Visitors arrive to an internet site according to a Poisson
process with an average of 10 visitors per hour. Use this
information to answer the following questions.
1.What is the probability that 12 visitors arrive in an hour?
(Use 4 decimal places)
2. What is the probability that at least 20 minutes elapse
between visitors to the website? (Use 4 decimal places)
3.What is the probability that at least 2 visitors come to the
website in 30 minutes? (Use 4...

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)...

A grocery store counts the number of customers who arrive during
an hour. The average over a year is 20 customers per hour. Assume
the arrival of customers follows a Poisson distribution. (It
usually does.)
Find the probability that at least one customer arrives in a
particular one minute period. Round your answer to 3
decimals.
Find the probability that at least two customers arrive in a
particular 4 minute period. Round your answer to four decimals.

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