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A steel manufacturer testing a new additive, for

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

Solution for problem 19SE Chapter 2

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 19SE

A steel manufacturer is testing a new additive for manufacturing an alloy of steel. The joint probability mass function of tensile strength (in thousands of pounds/in2) and additive concentration is

a. What are the marginal probability mass functions for X (additive concentration) and Y (tensile

strength)?

b. Are X and Y independent? Explain.

c. Given that a specimen has an additive concentration of 0.04, what is the probability that its strength is 150 or more?

d. Given that a specimen has an additive concentration of 0.08, what is the probability that its tensile strength is greater than 125?

e. A certain application calls for the tensile strength to be 175 or more. What additive concentration should be used to make the probability of meeting this specification the greatest?

Step-by-Step Solution:
Step 1 of 3

Answer:

Step1 of 5:

       Given data states that a steel manufacturer testing a new additive, for manufacturing an alloy of steel.

The joint probability mass function of tensile strength (y) and additive concentration (x).

                   

 

                   Tensile strength

Concentration of additive

 100

150

200

0.02

0.05

0.06

0.11

0.04

0.01

0.08

0.10

0.06

0.04

0.08

0.17

0.08

0.04

0.14

0.12


Step2 of 5:  

a). Here we need to find the marginal probability mass functions for X and Y.

                   

 

                   Tensile strength (y)

Concentration of additive (x)

 100

150

200

0.02

0.05

0.06

0.11

0.22

0.04

0.01

0.08

0.10

0.19

0.06

0.04

0.08

0.17

0.29

0.08

0.04

0.14

0.12

0.3

0.14

0.36

0.5

 

 

 The marginal probability mass function is found by summing along the rows of the joint probability mass function.

 For additive concentration (x): , , ,

     = 0 for

The marginal probability mass function is found by summing along the columns of the joint probability mass function.

For tensile strength (y):

 

= 0 for


Step2 of 5:

b). The aim is to find, X and Y are independent or not.

     

       In this case, X and Y are not independent.

       For example, but

                 

                                                           = 0.0308.

    Therefore,              

               

     So, X and Y are not independent.


 Step3 of 5:

c). Here we need to find the probability that its strength is 150 or more.

      We have a specimen has an additive concentration of 0.04.

    We use the conditional probability, that is

    

                                           

                                           

                                                            = 0.9474

           Therefore, the probability that specimen strength is 150 or more is 0.9474.


   Step4 of 5:

  d). To find the probability that its tensile strength is greater than 125.

      We have a specimen has an additive concentration of 0.08.

          We use the conditional probability, that is

    

                                         

                                           

                                             = 0.867

   Therefore, the probability that its tensile strength is greater than 125 is 0.867.


 

      Step5 of 5:

    e). Here we need to find, what additive concentration should be used to make the probability of meeting this specification the greatest.

         The tensile strength is greater than 175 if  Y

Step 2 of 3

Chapter 2, Problem 19SE is Solved
Step 3 of 3

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

This full solution covers the following key subjects: additive, Strength, concentration, Probability, tensile. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 19SE from 2 chapter was answered, more than 712 students have viewed the full step-by-step answer. The answer to “?A steel manufacturer is testing a new additive for manufacturing an alloy of steel. The joint probability mass function of tensile strength (in thousands of pounds/in2) and additive concentration is a. What are the marginal probability mass functions for X (additive concentration) and Y (tensilestrength)?b. Are X and Y independent? Explain.c. Given that a specimen has an additive concentration of 0.04, what is the probability that its strength is 150 or more?d. Given that a specimen has an additive concentration of 0.08, what is the probability that its tensile strength is greater than 125?e. A certain application calls for the tensile strength to be 175 or more. What additive concentration should be used to make the probability of meeting this specification the greatest?” is broken down into a number of easy to follow steps, and 123 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 19SE from chapter: 2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.

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