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The thickness of a washer (in mm) is a random variable

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

Solution for problem 23E Chapter 2.4

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 23E

The thickness of a washer (in mm) is a random variable with probability density function

a. What is the probability that the thickness is less than 2.5 m?

b. What is the probability that the thickness is between 2.5 and 3.5 m?

c. Find the mean thickness.

d. Find the standard deviation a of the thicknesses.

e. Find the probability that the thickness is within ±σ of the mean.

f. Find the cumulative distribution function of the thickness.

Step-by-Step Solution:

Step 1 of 6 :

The thickness of a washer is a random variable with the probability density function is

        

Our goal is to find :

a). What is the probability that the thickness is less than 2.5 m.

b). What is the probability that the thickness is between 2.5 and 3.5 m.

c). Find the mean thickness.

d). Find the standard deviation of the thickness.

e). Find the probability that the thickness is within of the mean.

f).  Find the cumulative distribution function of the thickness

a).

Now we have to find the probability that the thickness is less than 2.5 m.

The probability density function is

        

Here we take the limits 2 to 2.5.

P(x < 2.5)

Here we computing the indefinite integral.

Then,

P(x < 2.5)

We calculated the equation.

Then we get

P(x < 2.5)0.781252

P(x < 2.5)

P(x < 2.5)

Therefore the probability that the thickness is less than 2.5 m is 0.2428.

Step 2 of 6 :

b).

Now we have to find the probability that the thickness is between 2.5 and 3.5 m.

The probability density function is

        

Here we take the limits 2.5 to 3.5.

P(2.5< x < 3.5)

Here we computing the indefinite integral.

Then,

P(2.5< x < 3.5)

We calculated the equation.

Then we get.

P(2.5< x < 3.5)1.2567-0.781252

P(2.5< x < 3.5)1.29567-0.781252

P(2.5< x < 3.5)0.514418

Therefore the probability that the thickness is between 2.5 and 3.5 m is 0.514418.

Step 3 of 6 :

c).

Now we have to find the mean thickness.

Here we take the limits 2 to 4.

Then the mean  is

Here we computing the indefinite integral.

Then,

We calculated the equation.

Then we get.

Therefore the mean is 3.

Step 4 of 6

Chapter 2.4, Problem 23E is Solved
Step 5 of 6

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

The answer to “The thickness of a washer (in mm) is a random variable with probability density function a. What is the probability that the thickness is less than 2.5 m?________________b. What is the probability that the thickness is between 2.5 and 3.5 m?________________c. Find the mean thickness.________________d. Find the standard deviation a of the thicknesses.________________e. Find the probability that the thickness is within ±? of the mean.________________f. Find the cumulative distribution function of the thickness.” is broken down into a number of easy to follow steps, and 73 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: thickness, Probability, Find, function, mean. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 23E from chapter: 2.4 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. Since the solution to 23E from 2.4 chapter was answered, more than 1348 students have viewed the full step-by-step answer.

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