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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi
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A steel manufacturer testing a new additive, for

Chapter 2, Problem 19SE

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QUESTION:

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?

Questions & Answers

QUESTION:

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?

ANSWER:

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)

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