Question

On average, a financial aid counselor can see students at a rate of 5.75 per hour. Counseling session time is thought to follow the exponential probability distribution. Find the following probabilities

a) the probability that service time is less than 8 minutes

b) the probability that service time exceeds 13 minutes

c) the probability that service time is exactly 10 minutes

d) the probability that service time is between 9 and 15 minutes

Answer #1

In a car pressure wash the average arrival rate is 12 cars per
hour and are serviced at an average rate of 15 cars per hour, with
service times exponential.
It is requested:
a) Probability that the system is empty.
b) Average number of clients in the washing system.
c) Average number of clients in the row.
d) Average time a customer waits in line.
e) Probability of having a row of more than 2 clients.
f) Probability of waiting...

-On the weekend, emergency services average four
patients per hour, and the service rate is expected to be 40
minutes.
How many nurses will be needed to achieve an average
time in the line of 30 minutes or less? [ Poisson
Distrubution]

Exponential/Poisson
Megacity Bank operates a drive-up teller window that
allows customers to complete bank transactions without having to
get out of their car. Megacity Bank waiting line times follow an
exponential distribution with a service rate of 36 customers per
hour.
A.What is the probability that the time to service is 1 minute
or less? (show your formula with the numbers plugged in, as well as
the answer. You may use the e^(-λ) table, an advanced calculator or
excel to...

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)...

Students arrive at the Administrative Services Office at an
average of one every 15 minutes, and their requests take on average
10 minutes to be processed. The service counter is staffed by only
one clerk, Judy Gumshoes, who works eight hours per day. Assume
Poisson arrivals and exponential service times.
a. What percentage of time is Judy idle?
(Round your answer to 1 decimal place.)
Percentage of time
%
b. How much time, on average, does a student spend
waiting...

At a 24-hour computer repair facility broken-down computers
arrive at an average rate of 3 per day, Poisson distributed.
What is the probability that on a given day no computers arrive
for repair?
What is the probability that on a given day at least 3
computers arrive for repair?
What is the distribution of the time between arrivals of
computers to this facility and what is the average time between
arrivals?
On one particular day no computer has arrived for...

A car manufacturer has determined it takes an average time of 56
minutes to produce a car. The population standard deviation is
assumed to be 6 minutes. The company pays a bonus to the workers
for every car produced in 48 minutes or less. Assuming that the
production time is normally distributed, answer the following
questions. Let X = production time of a randomly selected car.
Round all probabilities to four decimal places and times
to two decimal places.
a)...

A car manufacturer has determined it takes an average time of 51
minutes to produce a car. The population standard deviation is
assumed to be 7 minutes. The company pays a bonus to the workers
for every car produced in 43 minutes or less. Assuming that the
production time is normally distributed, answer the following
questions. Let X = production time of a randomly selected car.
(Round probabilities to four decimals and times to two
decimals.)
a) What is the...

Problem 11-15
(Algorithmic)
Ocala Software Systems
operates a technical support center for its software customers. If
customers have installation or use problems with Ocala software
products, they may telephone the technical support center and
obtain free consultation. Currently, Ocala operates its support
center with one consultant. If the consultant is busy when a new
customer call arrives, the customer hears a recorded message
stating that all consultants are currently busy with other
customers. The customer is then asked to hold...

Ocala Software Systems operates a technical support center for
its software customers. If customers have installation or use
problems with Ocala software products, they may telephone the
technical support center and obtain free consultation. Currently,
Ocala operates its support center with one consultant. If the
consultant is busy when a new customer call arrives, the customer
hears a recorded message stating that all consultants are currently
busy with other customers. The customer is then asked to hold and
is told...

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