×
Log in to StudySoup
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.5 - Problem 15e
Join StudySoup for FREE
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.5 - Problem 15e

Already have an account? Login here
×
Reset your password

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

  • Textbook Solutions
  • 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 | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

4 5 1 365 Reviews
11
4
Problem 15E

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:

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

  1.  P(X<9.98)
  2.  P(Y> 5.01)
  3.  P(X<9.98 and Y>5.01)
  4.  E(X)
  5.  E(Y)

Step  2:

   

   

  1. 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:

(d) we have to find the mean of X

                         

                                  E(x) = x f(x) dx

                                       =  10 x dx

                                       =  10 [

                                       =  5 ( 2)

                                       =   10

Therefore the mean value of x , E(x) =10

(e)   We have to find the mean of Y

                                E(y) =   y f(y)dy

                                     =   dy

   

                                     =  5 [

                                      =  2.5 [2]

                                      = 5

Therefore the mean of Y, E(y)= 5.


                           

           

           

Step 2 of 3

Chapter 2.5, Problem 15E is Solved
Step 3 of 3

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 1422 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.

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

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