The answer to Exercise 19 part (d) is needed for this

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

ISBN: 9780073401331 38

Solution for problem 20SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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Problem 20SE

The answer to Exercise 19 part (d) is needed for this exercise. A geologist counts 64 emitted particles in one minute from a certain radioactive rock.

a. Find a 95% confidence interval for the rate of emissions in units of particles per minute.

b. After four minutes, 256 particles are counted. Find a 95% confidence interval for the rate of emissions in units of particles per minute.

c. For how many minutes should errors be counted in order that the 95% confidence interval specifies the rate to within ± 1 particle per minute?

Step-by-Step Solution:

Step 1 of 3</p>

a) The no. of emitted particles counted by geologist is 64

Here we have to find the 95% confidence intervals

The 95% confidence intervals are $\ \widehat{\lambda{}}\pm{}Z{\ }_{\alpha{}/2}\sqrt{\frac{\widehat{\lambda{}}}{n}}$

$Z{\ }_{\alpha{}/2}$ is the critical value at 5% level of significance

Then $Z{\ }_{\alpha{}/2}$ =1.96

Here X=64, n=1, $\widehat{\lambda{}}=X/n$ =64

Then $64\pm{}$ 1.96 $\sqrt{\frac{64}{1}}$ = 64 $\pm{}15.68$

=(48.62, 79.68)

Hence the 95% confidence intervals are (48.62, 79.68)

Step 2 of 3</p>

b) 256 particles emitted in 4 minutes

The 95% confidence intervals are $\ \widehat{\lambda{}}\pm{}Z{\ }_{\alpha{}/2}\sqrt{\frac{\widehat{\lambda{}}}{n}}$

$Z{\ }_{\alpha{}/2}$ is the critical value at 5% level of significance

Then $Z{\ }_{\alpha{}/2}$ =1.96

Here X=256, n=4

$\widehat{\lambda{}}=X/n$ =256/4

=64

The 95% confidence intervals are $\ \widehat{\lambda{}}\pm{}Z{\ }_{\alpha{}/2}\sqrt{\frac{\widehat{\lambda{}}}{n}}$ = $64\pm{}1.96\sqrt{64/4}$

= $64\pm{}7.86$

=(56.14, 71.84)

Hence the 95% confidence intervals are (56.14, 71.84)

Step 3 of 3

Chapter 5, Problem 20SE is Solved

Textbook: Statistics for Engineers and Scientists

Edition: 4

Author: William Navidi

ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 20SE from chapter: 5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: particles, minute, confidence, interval, rate. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 20SE from 5 chapter was answered, more than 262 students have viewed the full step-by-step answer. The answer to “The answer to Exercise 19 part (d) is needed for this exercise. A geologist counts 64 emitted particles in one minute from a certain radioactive rock.a. Find a 95% confidence interval for the rate of emissions in units of particles per minute.________________b. After four minutes, 256 particles are counted. Find a 95% confidence interval for the rate of emissions in units of particles per minute.________________c. For how many minutes should errors be counted in order that the 95% confidence interval specifies the rate to within ± 1 particle per minute?” is broken down into a number of easy to follow steps, and 90 words.