Question
In: Statistics and Probability
Suppose that the number of requests for assistance received by a towing service is a Poisson...
Suppose that the number of requests for assistance received by a towing service is a Poisson process with rate α = 6 per hour.
a) Find expected value and variance of the number of requests in 30-minutes. Then compute the probability that there is at most one request in 30-minute interval. Clearly state the random variable of interest using the context of the problem and what probability distribution it follows.
b) What is the probability that more than 20 minutes elapse between two successive requests? Clearly state the random variable of interest using the context of the problem and what probability distribution it follows.
Solutions
orchestra answered 1 year agoRelated Solutions
2.) Suppose that the number of requests for assistance received by a towing service is a...
2.) Suppose that the number of requests for assistance received
by a towing service is a Poisson process with rate a = 6 per
hour.
a.) Find the expected value and variance of the number of
requests in 30 minutes. Then compute the probability that there is
at most one request in 30 minute interval.
b.) What is the probability that more than 20 minutes elapse
between two successive requests? Clearly state the random variable
of interest using the context...
The reference desk of a university library receives requests for assistance. Assume that a Poisson probability...
The reference desk of a university library receives requests for
assistance. Assume that a Poisson probability distribution with an
arrival rate of 11 requests per hour can be used to describe the
arrival pattern and that service times follow an exponential
probability distribution with a service rate of 15 requests per
hour. (Round your answers to four decimal places.)
(a)
What is the probability that no requests for assistance are in
the system?
(b)
What is the average number of...
The reference desk of a university library receives requests for assistance. Assume that a Poisson probability...
The reference desk of a university library receives requests for
assistance. Assume that a Poisson probability distribution with an
arrival rate of 8 requests per hour can be used to describe the
arrival pattern and that service times follow an exponential
probability distribution with a service rate of 11 requests per
hour.
What is the probability that no requests for assistance are in
the system? If required, round your answer to four decimal
places.
P0 = ??
What is the...
The reference desk of a university library receives requests for assistance. Assume that a Poisson probability...
The reference desk of a university library receives requests for
assistance. Assume that a Poisson probability distribution with an
arrival rate of 9 requests per hour can be used to describe the
arrival pattern and that service times follow an exponential
probability distribution with a service rate of 11 requests per
hour.
What is the probability that no requests for assistance are in
the system? If required, round your answer to four decimal
places.
P0 =
What is the average...
2a). The customer service department of H&R Block received a total of 235 telephone requests for...
2a). The customer service department
of H&R Block received a total of 235 telephone requests for a
tip-sheet on personal tax or corporate tax. The following table
summarizes callers' primary area of interest, and how they first
heard about the tip-sheet.
Topic of most interest to caller
How the caller first heard about the report
Radio
Newspaper
Television
Internet
Personal tax
34
20
26
20
Corporate tax
36
70
14
15
What is the probability a caller is
interested in...
The number of complaints received by a company each month follows a Poisson distribution with mean...
The number of complaints received by a company each month
follows a Poisson distribution
with mean 6.
(a) Calculate the probability the company receives no complaint in
a certain week.
(b) Calculate the probability the company receives more than 4
complaints in a 2-week
period.
(c) Over a certain month, calculate the probability the company
receives fewer complaints
than it usually does with respect to its monthly average.
Suppose the number of customers arriving in a bookstore is Poisson distributed with a mean of...
Suppose the number of customers arriving in a bookstore is
Poisson distributed with a mean of 2.3 per 12 minutes. The manager
uses a robot to observe the customers coming to the bookstore.
a)What is the mean and variance of the number of customers coming
into the bookstore in 12 minutes? b)What is the probability that
the robot observes 10 customers come into the bookstore in one
hour? c)What is the probability that the robot observes at least
one customer...
2) Suppose the number of typos in the rough draft of a document is a Poisson...
2) Suppose the number of typos in the rough draft of a document
is a Poisson random variable with an expected value of 1 typo per
page. What is the probability that one page of the document has at
least 1 typo?
Suppose that the number of accidents occurring in an industrial plant is described by a Poisson...
Suppose that the number of accidents occurring in an industrial
plant is described by a Poisson distribution with an average of 1.5
accidents every three months. Find the probability that
no accidents will occur during the current three-month
period.
less than 2 accidents will occur during a particular year
The breaking strength of plastic bags used for packaging is
normally distributed, with a mean of 5 pounds per square inch and a
standard deviation of 1.5 pounds per square inch....
1. The number of missed notes by a musician in a symphony is Poisson. Suppose the...
1. The number of missed notes by a musician in a symphony is
Poisson. Suppose the principle trombonist misses an average of 2
notes per concert, and the 2nd trombonist misses an average of 5
notes per concert.
(a) What is the probability that they miss no notes in a
concert?
(b) Suppose a concert requires only one trombonist and there is
an even chance either is chosen. What is the probability no notes
are missed in that concert?
(c)...
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