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The thickness Xof a wooden shim (in mm) has probability

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

Solution for problem 16E Chapter 2.5

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 16E

Problem 16E

The thickness Xof a wooden shim (in mm) has probability density function

a. Find μX

b. Find

c. Let Y denote the thickness of a shim in inches (1 mm = 0.0394 inches). Find μγ and

d. If three shims are selected independently and stacked one atop another, find the mean and variance of the total thickness.

Step-by-Step Solution:
Step 1 of 3

Solution 16E

Step1 of 5:

We have a random variable X it presents the thickness of wooden shim and it has a probability density function:

Here Our goal is:

a).We need to find

b).We need to find

c).We need to Find  and by taking Y as the thickness of a shim in inches (1 mm = 0.0394 inches).

d). If three shims are selected independently and stacked one atop another, find the mean and variance of the total thickness.


Step2 of 5:

a).

      =

      =  

      =     [therefore ]

      =

      =

 =

 =

 = -27 - (-32)

 = -27 + 32

 = 5

Hence, = 5.


Step3 of 5:

b).

   =

  =  

 =        [therefore ]

 =

 =

 =

 =

 =

 =

 = 25.2

Hence, = 25.2.

Now,

     = 25.2 -

     = 25.2 - 25

     = 0.2

Hence, = 0.2.


Step4 of 5:

c).

We have c = 0.0394

 

       

 = c

         = 0.0394(5)

       = 0.197

Hence, = 0.197.

 

        =

        = 3.1047

Hence,  = 3.1047.


Step5 of 5:

d).

Let us consider are three thicknesses of wooden shim.

Let Z = be the total thickness.

Now,

      = 3

      = 3(5)

      = 15

Hence, = 15.

       = 3()

       = 3(0.2)

       = 0.6

Hence, = 0.6.


 

 

Step 2 of 3

Chapter 2.5, Problem 16E is Solved
Step 3 of 3

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

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