Question

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?

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.

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 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 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 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?

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?

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.

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...

In a grocery store, there is one cashier counter. Customers
arrive at the cashier counter according to a Poisson process. The
arrival rate is 30 customers per hour. The service time is
exponentially distributed. The mean service time is 1 minute 30
seconds.
1. What is the expected number of customers waiting in the
system.
2. What is the expected waiting time.( unit in minutes)
3. What is the utilization rate (unit in %) of
the cashier?

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...

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