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Measurements are made on the length and width (in cm) of a

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

Solution for problem 15E 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 15E

Measurements are made on the length and width (in cm) of a rectangular component. Because of measurement error, the measurements are random variables. Let X denote the length measurement and let Y denote the width measurement. Assume that the probability density function of X is

and that the probability density function of Y is

Assume that the measurements X and Y are independent.

a. Find P(X<9.98).

b. Find P(Y > 5.01).

c. Find P(X<9.98 and Y > 5.01).

d. Find μX.

e. Find μγ.

Step-by-Step Solution:

Step 1:

Let X denote the length measurement and let Y denote the width measurement. Here the probability density function of X is

                   

And the density function of Y is

                     

We have to find

 P(X<9.98) P(Y> 5.01) P(X<9.98 and Y>5.01) E(X) E(Y)

Step  2:

   

   

We have to find the probability P(X<9.98)

           P(X<9.98) = f(x)  dx

       

                            =  

                            =   10 [X

                            =  10 (9.98-9.95)

       

                             = 0.3.

  Therefore the probability P(X<9.98) is 0.3.

(b)  We have to find the probability that P(Y>5.01)

        P(Y>5.01) =  f(y) dy

                        =   5 dy

                        =   5 [y

                        =  5 [5.1-5.01]

                          =  0.45

Therefore the probability P(Y>5.01)  is 0.45.

(c)   We have to find the probability that P(X<9.98 and Y>5.01)

       

          Since the measurements X and Y are independent

 

          P(X<9.98 and Y>5.01) = P(X<9.98) P(Y>5.01)

                                          =  (0.3) (0.45)

                                          = 0.135

Step 3 of 3

Chapter 2.5, Problem 15E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The full step-by-step solution to problem: 15E from chapter: 2.5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “Measurements are made on the length and width (in cm) of a rectangular component. Because of measurement error, the measurements are random variables. Let X denote the length measurement and let Y denote the width measurement. Assume that the probability density function of X is and that the probability density function of Y is Assume that the measurements X and Y are independent.a. Find P(X<9.98).________________b. Find P(Y > 5.01).________________c. Find P(X<9.98 and Y > 5.01).________________d. Find ?X.________________e. Find ??.” is broken down into a number of easy to follow steps, and 79 words. Since the solution to 15E from 2.5 chapter was answered, more than 983 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: Find, measurements, measurement, Density, Probability. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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