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Solved: Cabs pass your workplace according to a Poisson

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 110E Chapter 4.7

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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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.

Step-by-Step Solution:

Answer

Step 1 of 4</p>

(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.

Step 2 of 4</p>

(b)

We are asked to approximate the probability that more than  pass within a

We need to find the probability

If  is a Poisson random variable with  and

Is approximately a standard normal variable.

The same continuity correction of used for the binomial distribution can also be applied.

The approximation is good for

This probability can be expressed exactly as

The computational difficulty is clear. Hence the probability can be approximated after continuity correction of  as

From the z table, the area to the left of  is .

Hence the approximate probability that more than  pass within a  is

Step 3 of 4

Chapter 4.7, Problem 110E is Solved
Step 4 of 4

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

The answer to “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.” is broken down into a number of easy to follow steps, and 80 words. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. This full solution covers the following key subjects: cabs, Pass, mean, Probability, day. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Since the solution to 110E from 4.7 chapter was answered, more than 1207 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 110E from chapter: 4.7 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM.

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