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# You have received a radioactive mass that is claimed to

## Problem 18E Chapter 4.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 18E

Problem 18E

You have received a radioactive mass that is claimed to have a mean decay rate of at least 1 particle per second. If the mean decay rate is less than 1 per second, you may return the product for a refund. Let X be the number of decay events counted in 10 seconds.

a. If the mean decay rate is exactly 1 per second (so that the claim is true, but just barely), what is P(X ≤ 1)?

b. Based on the answer to part (a), if the mean decay rate is 1 particle per second, would one event in 10 seconds be an unusually small number?

c. If you counted one decay event in 10 seconds, would this be convincing evidence that the product should be returned? Explain.

d. If the mean decay rate is exactly 1 per second, what is P(X ≤ 8)?

e. Based on the answer to part (d), if the mean decay rate is 1 particle per second, would eight events in 10 seconds be an unusually small number?

f. if  you counted eight decay events in 10 seconds would this be convincing evidence that the product should be returned? Explain.

Step-by-Step Solution:

Step 1 of 7</p>

Let X be the No. of decay events counted in 10 seconds

Here XPoisson(10)

The pmf of poisson distribution is P(x)=,  x=0,1,2,.......

Step 2 of 7</p>

a)We have to find P(x1) if the mean decay rate is exactly 1 per second

Now  P(x1)=P(0)+P(1)

=+

=0.000045+0.00045

=0.0005

if the mean decay rate is exactly 1 per second P(x1)=0.0005

Step 3 of 7</p>

b) Yes , if the mean decay rate is exactly 1 per second

one event in 10 seconds is unusually a small number

Because it occurs once in 2000 cases

Step 4 of 7</p>

c) Yes, this is the convincing evidence that the product should be returned

Because the probability is only 0.0005

And if the mean decay rate is exactly 1 per second

one event in 10 seconds is unusually a small number

Step 5 of 7

Step 6 of 7

##### ISBN: 9780073401331

The full step-by-step solution to problem: 18E from chapter: 4.3 was answered by Patricia, 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: 4th. Since the solution to 18E from 4.3 chapter was answered, more than 356 students have viewed the full step-by-step answer. This full solution covers the following key subjects: decay, mean, rate, seconds, particle. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9780073401331. The answer to “You have received a radioactive mass that is claimed to have a mean decay rate of at least 1 particle per second. If the mean decay rate is less than 1 per second, you may return the product for a refund. Let X be the number of decay events counted in 10 seconds.a. If the mean decay rate is exactly 1 per second (so that the claim is true, but just barely), what is P(X ? 1)?________________b. Based on the answer to part (a), if the mean decay rate is 1 particle per second, would one event in 10 seconds be an unusually small number?________________c. If you counted one decay event in 10 seconds, would this be convincing evidence that the product should be returned? Explain.________________d. If the mean decay rate is exactly 1 per second, what is P(X ? 8)?________________e. Based on the answer to part (d), if the mean decay rate is 1 particle per second, would eight events in 10 seconds be an unusually small number?________________f. if you counted eight decay events in 10 seconds would this be convincing evidence that the product should be returned? Explain.” is broken down into a number of easy to follow steps, and 190 words.

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