/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q26E Automated electron backscattered... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q26E (page 28)

Automated electron backscattered diffraction is now being used in the study of fracture phenomena. The following information on misorientation angle (degrees) was extracted from the article 鈥淥bservations on the Faceted Initiation Site in the Dwell-Fatigue Tested Ti-6242 Alloy: Crystallographic Orientation and Size Effects鈥� (Metallurgical and Materials Trans., 2006: 1507鈥�1518).

Class: 0-<5 5-<10 10-<15 15-<20

Relfreq: .177 .166 .175 .136

Class: 20-<30 30-<40 40-<60 60-<90

Relfreq: .194 .078 .044 .030

a. Is it true that more than 50% of the sampled angles are smaller than 15掳, as asserted in the paper?

b. What proportion of the sampled angles are at least 30掳?

Short Answer

Expert verified

a.

Yes, it is true that more than 50% of the sampled angles are smaller than 15掳, as asserted in the paper.

b.

The percentage of the sampled angles that are at least 30 degrees is 0.152.

Step by step solution

01

Given information

The data for the misorientation angle (degrees) is provided.

02

Check the proportion

The relative frequency table is given as,

Class

Relative frequency

0-5

0.177

5-10

0.166

10-15

0.175

15-20

0.136

20-30

0.194

30-40

0.078

40-60

0.044

60-90

0.030

a.

Let x represents the sampled angles.

The proportion of the sampled angles that are smaller than 15 degrees is computed as,

\(\begin{aligned}P\left( {x < 15} \right) &= P\left( {0 - 5} \right) + P\left( {5 - 10} \right) + P\left( {10 - 15} \right)\\ &= 0.177 + 0.166 + 0.175\\ &= 0.518\end{aligned}\)

Therefore, the percentage of the sampled angles that are smaller than 15 degrees is 51.8% which is more than 50%.

Yes, it is true that more than 50% of the sampled angles are smaller than 15掳, as asserted in the paper.

03

Given information

The data for the misorientation angle (degrees) is provided.

04

Compute the proportion

The relative frequency table is given as,

Class

Relative frequency

0-5

0.177

5-10

0.166

10-15

0.175

15-20

0.136

20-30

0.194

30-40

0.078

40-60

0.044

60-90

0.030

b.

Let x represents the sampled angles.

The proportion of the sampled angles that are atleast 30 degrees is computed as,

\(\begin{aligned}P\left( {x \ge 30} \right) &= P\left( {30 - 40} \right) + P\left( {40 - 60} \right) + P\left( {60 - 90} \right)\\ &= 0.078 + 0.044 + 0.030\\ &= 0.152\end{aligned}\)

Therefore, the percentage of the sampled angles that are at least 30 degrees is 0.152.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In 1997 a woman sued a computer keyboard manufacturer,charging that her repetitive stress injuries werecaused by the keyboard (Genessy v. Digital EquipmentCorp.).The injury awarded about \(3.5 million for painand suffering, but the court then set aside that awardas being unreasonable compensation. In making this determination, the court identified a 鈥渘ormative鈥� group of27 similar cases and specified areasonable award as onewithin two standard deviations of the mean of the awardsin the 27 cases. The 27 awards were (in \)1000s) 37, 60,75, 115, 135, 140, 149, 150, 238, 290, 340, 410, 600, 750,750, 750, 1050, 1100, 1139, 1150, 1200, 1200, 1250,1576, 1700, 1825, and 2000, from which\(\sum {{x_i} = } \)20,179,\(\sum {x_i^2} = 24,657,511\). What is the maximum possible amount that could be awarded under the two- standard deviation rule?

a. Give three different examples of concrete populations and three different examples of hypothetical populations.

b. For one each of your concrete and your hypothetical populations, give an example of a probability question and an example of an inferential statistics question.

Compute the sample median, 25% trimmed mean, 10% trimmed mean, and sample mean for the lifetime data given in Exercise 27, and compare these measures.

The weekly demand for propane gas (in \({\rm{1000s}}\) of gallons) from a particular facility is an \({\rm{rv}}\) \({\rm{X}}\) with pdf

\({\rm{f(x) = }}\left\{ {\begin{array}{*{20}{c}}{{\rm{2}}\left( {{\rm{1 - }}\frac{{\rm{1}}}{{{{\rm{x}}^{\rm{2}}}}}} \right)}&{{\rm{1}} \le {\rm{x}} \le {\rm{2}}}\\{\rm{0}}&{{\rm{ otherwise }}}\end{array}} \right.\)

a. Compute the cdf of \({\rm{X}}\).

b. Obtain an expression for the \({\rm{(100p)th}}\) percentile. What is the value of \({\rm{\tilde \mu }}\)?

c. Compute \({\rm{E(X)}}\) and \({\rm{V(X)}}\).

d. If \({\rm{1}}{\rm{.5}}\) thousand gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the \({\rm{1}}{\rm{.5}}\) thousand gallons is expected to be left at the end of the week? (Hint: Let \({\rm{h(x) = }}\) amount left when demand \({\rm{ = x}}\).)

Two airplanes are flying in the same direction in adjacent parallel corridors. At time \({\rm{t = 10}}\), the first airplane is \({\rm{10}}\)km ahead of the second one. Suppose the speed of the first plane (km/hr.) is normally distributed with mean \({\rm{520\;}}\)and standard deviation \({\rm{10}}\) and the second plane鈥檚 speed is also normally distributed with mean and standard deviation \({\rm{500\; and\; 10}}\), respectively.

a. What is the probability that after \({\rm{2hr}}{\rm{. }}\)of flying, the second plane has not caught up to the first plane?

b. Determine the probability that the planes are separated by at most \({\rm{10km\; after\; 2hr}}{\rm{. }}\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.