A manufacturer claims that the tensile strength of a

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

ISBN: 9780073401331 38

Solution for problem 10E Chapter 4.6

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 10E

A manufacturer claims that the tensile strength of a certain composite (in MPa) has the lognormal distribution with μ = 5 and a σ= 0.5. Let X be the strength of a randomly sampled specimen of this composite.

a.If the claim is true, what is P(X<20)?

b.Based on the answer to part (a), if the claim is true, would a strength of 20 MPa be unusually small?

c. If you observed a tensile strength of 20 MPa, would this be convincing evidence that the claim is false? Explain.

d. If the claim is true, what is P(X<130)?

e. Based on the answer to part (d), if the claim is true, would a strength of 130 MPa be unusually small?

f.If you observed a tensile strength of 130 MPa, would this be convincing evidence that the claim is false? Explain.

Step-by-Step Solution:

Step 1 of 7</p>

Let X be the strength of the composite

Here the claim is the tensile strength is has a lognormal distribution with $\mu{}=5$ and $\sigma{}=0.5$

X follows the lognormal distribution with mean $\mu{}=5$

And standard deviation $\sigma{}{\ }^{\ }$ =0.5

Step 2 of 7</p>

a) We have to find $P(X<20)$ if the claim is true

$P(X<20)=P(ln\ X<ln\ 20)$

= $P(ln\ X<2.9957)$

We have to find the Z score for 2.9957

Then Z= $(\overline{X}-\mu{})/\sigma{}$

=(2.9957-5)/0.5

= -4.0086

Now P(X<20)=P(Z< -4.01)

=0.00003

Hence P(X<20)=0.00003

Step 3 of 7</p>

b) Yes, The strength of 20 MPa is unusually small

Because this occurs 3 in 100000 samples

Step 4 of 7</p>

c) Yes this the convincing evidence that the claim is false

Because the probability is very small

And the strength of 20 MPa is unusually small

Step 5 of 7

Chapter 4.6, Problem 10E is Solved

Step 6 of 7

Textbook: Statistics for Engineers and Scientists

Edition: 4

Author: William Navidi

ISBN: 9780073401331

Since the solution to 10E from 4.6 chapter was answered, more than 233 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 10E from chapter: 4.6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: claim, Strength, mpa, true, tensile. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “A manufacturer claims that the tensile strength of a certain composite (in MPa) has the lognormal distribution with ? = 5 and a ?= 0.5. Let X be the strength of a randomly sampled specimen of this composite.a.If the claim is true, what is P(X<20)?________________b.Based on the answer to part (a), if the claim is true, would a strength of 20 MPa be unusually small?________________c. If you observed a tensile strength of 20 MPa, would this be convincing evidence that the claim is false? Explain.________________d. If the claim is true, what is P(X<130)?________________e. Based on the answer to part (d), if the claim is true, would a strength of 130 MPa be unusually small?________________f.If you observed a tensile strength of 130 MPa, would this be convincing evidence that the claim is false? Explain.” is broken down into a number of easy to follow steps, and 133 words.