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A physicist wants to estimate the rate of emissions of

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 20E Chapter 4.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 20E

A physicist wants to estimate the rate of emissions of alpha particles from a certain source. He makes two counts. First, he measures the background rate by counting the number of particles in 100 seconds in the absence of the source. He counts 36 background emissions. Then, with the source present, he counts 324 emissions in 100 seconds. This represents the sum of source emissions plus background emissions.

a. Estimate the background rate, in emissions per second, and find the uncertainty in the estimate.

b. Estimate the sum of the source plus background rate, in emissions per second, and find the uncertainty in the estimate.

c. Estimate the rate of source emissions in particles per second, and find the uncertainty in the estimate.

d. Which will provide the smaller uncertainty in estimating the rate of emissions from the source: (1) counting the background only for 150 seconds and the background plus the source for 150 seconds, or (2) counting the background for 100 seconds and the source plus the background for 200 seconds? Compute the uncertainty in each case.

e. Is it possible to reduce the uncertainty to 0.03 particles per second if the background rate is measured for only 100 seconds? If so, for how long must the source plus background be measured? If not, explain why not.

Step-by-Step Solution:

Step 1 of 6</p>

First a physicist counts 36 background emissions in 100 seconds

Next with the help of source he counts 324 emissions in 100 seconds

Let represents the rate of emissions in the background per second

Let represents the rate of emissions in presence of source per second

Let represents the rate of total emissions per second

Step 2 of 6</p>

a) Here we have to estimate the background rate of emissions in one second and the uncertainty in the estimate

Let X be the no. of emissions

Per one second the no. of emissions are 36/100=0.36

Here Xpoisson (0.36)

The estimated=0.36

The uncertainty is  

                                   =

                                   =0.06

The uncertainty in the estimate is 0.06

           

The estimated background rate of emissions

Step 3 of 6</p>

b) Here we have to estimate the sum of source plus background rate of emissions in one second and the uncertainty in the estimate

the rate of emissions in the background =0.36

the rate of emissions in presence of source =324/100

                                                                           =3.24

The total rate of emissions is

                                                     =0.36+3.24

                                                     =3.6

The uncertainty in the background is =0.06

                           

The uncertainty in the presence of source is  

                                                                              =

                                                                              =0.18

The uncertainty in the total emissions is   

                                                                         =

                                                                         =0.0626

The total estimated rate of emissions

Step 4 of 6

Chapter 4.3, Problem 20E is Solved
Step 5 of 6

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This full solution covers the following key subjects: background, source, emissions, estimate, seconds. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 20E from chapter: 4.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “A physicist wants to estimate the rate of emissions of alpha particles from a certain source. He makes two counts. First, he measures the background rate by counting the number of particles in 100 seconds in the absence of the source. He counts 36 background emissions. Then, with the source present, he counts 324 emissions in 100 seconds. This represents the sum of source emissions plus background emissions.a. Estimate the background rate, in emissions per second, and find the uncertainty in the estimate.________________b. Estimate the sum of the source plus background rate, in emissions per second, and find the uncertainty in the estimate.________________c. Estimate the rate of source emissions in particles per second, and find the uncertainty in the estimate.________________d. Which will provide the smaller uncertainty in estimating the rate of emissions from the source: (1) counting the background only for 150 seconds and the background plus the source for 150 seconds, or (2) counting the background for 100 seconds and the source plus the background for 200 seconds? Compute the uncertainty in each case.________________e. Is it possible to reduce the uncertainty to 0.03 particles per second if the background rate is measured for only 100 seconds? If so, for how long must the source plus background be measured? If not, explain why not.” is broken down into a number of easy to follow steps, and 214 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 20E from 4.3 chapter was answered, more than 613 students have viewed the full step-by-step answer.

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