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Solved: Cabs pass your workplace according to a Poisson
Chapter 4, Problem 110E(choose chapter or problem)
Problem 110E
Cabs pass your workplace according to a Poisson process with a mean of five cabs per hour.
(a) Determine the mean and standard deviation of the number of cabs per 10-hour day.
(b) Approximate the probability that more than 65 cabs pass within a 10-hour day.
(c) Approximate the probability that between 50 and 65 cabs pass in a 10-hour day.
(d) Determine the mean hourly rate so that the probability is approximately 0.95 that 100 or more cabs pass in a 10-hour data.
Questions & Answers
QUESTION:
Problem 110E
Cabs pass your workplace according to a Poisson process with a mean of five cabs per hour.
(a) Determine the mean and standard deviation of the number of cabs per 10-hour day.
(b) Approximate the probability that more than 65 cabs pass within a 10-hour day.
(c) Approximate the probability that between 50 and 65 cabs pass in a 10-hour day.
(d) Determine the mean hourly rate so that the probability is approximately 0.95 that 100 or more cabs pass in a 10-hour data.
ANSWER:
Answer
Step 1 of 4
(a)
Cabs pass your workspace according to a Poisson process with a mean of five cabs per hour.
We are asked to find the mean and standard deviation of the number of cabs per
Let denote the number of cabs per
. Then,
has a Poisson distribution with
……(1)
If is a Poisson random variable over an interval of length
with parameter
, then
Using equation (1), we can write the mean and variance,
Hence standard deviation,
Hence the mean and standard deviation of the number of cabs per is
respectively.