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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.5 - Problem 16e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.5 - Problem 16e

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# The thickness Xof a wooden shim (in mm) has probability ISBN: 9780073401331 38

## Solution for problem 16E Chapter 2.5

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

Step 3 of 3

##### ISBN: 9780073401331

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