# The main bearing clearance (in mm) in a certain type of ## Problem 20E Chapter 2.4

Statistics for Engineers and Scientists | 4th Edition

• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants Statistics for Engineers and Scientists | 4th Edition

4 5 0 266 Reviews
22
4
Problem 20E

The main bearing clearance (in mm) in a certain type of engine is a random variable with probability density function a. What is the probability that the clearance is less than 0.02 mm?

b. Find the mean clearance.

c. Find the standard deviation of the clearances.

d. Find the cumulative distribution function of the clearance.

e. Find the median clearance.

f. The specification for the clearance is 0.015 to 0.063 mm. What is the probability that the specification is met?

Step-by-Step Solution:

Step 1 of 6 :

The main bearing clearance in a in a certain type of engine is a random variable with the probability density function is Our goal is to find :

a). What is the probability that the clearance is less than 0.02 mm?

b). Find the mean clearance.

c). Find the standard deviation of the clearance.

d). Find the cumulative distribution function of the clearance.

e). Find the median clearance.

f). Find the probability that the specification is met.

a).

Now we have to find the probability that the clearance is less than 0.02 mm.

So P(X < 0.02) is

The probability density function is Here we take the limits 0 to 0.02.

Then,

P(X < 0.02) = We are integrating.

P(X < 0.02) = P(X < 0.02) = P(X < 0.02) = P(X < 0.02) = P(X < 0.02) = Therefore the probability that the clearance is less than 0.02 mm is 0.125.

Step 2 of 6 :

b).

Now we have to find the mean clearance.

Mean is Here the limits is 0 to 0.04 and 0.04 to 0.08.  Or  We integrate the above equation and we substituted that equation.   Then we get the mean value. Therefore the mean value is 0.04.

Step 3 of 6 :

c).

Now we have to find the standard deviation of the clearance.

We are applying the limits 0 to 0.04 and 0.04 to 0.08.

The variance is      We integrate the above equation and we substituted that equation.

Then we get the variance value. Standard deviation is the square root of the variance.  Therefore the standard deviation of the clearance is 0.01634.

Step 4 of 6

Step 5 of 6

##### ISBN: 9780073401331

Unlock Textbook Solution

The main bearing clearance (in mm) in a certain type of

×
Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 2.4 - Problem 20e

Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 2.4 - Problem 20e

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
We're here to help