Problem 1. The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of pene tration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. (Rockwell hardness is measured on a continuous scale.) a) If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Problem 1. The Rockwell hardness of a metal is determined by impressing a
hardened point into the surface of the metal and then measuring the depth of pene
tration of the point. Suppose the Rockwell hardness of a particular alloy is normally
distributed with mean 70 and standard deviation 3. (Rockwell hardness is measured
on a continuous scale.)
a) If a specimen is acceptable only if its hardness is between 67 and 75, what is
the probability that a randomly chosen specimen has an acceptable hardness?
b) If two alloys are randomly selected, which is the probability that one will have
Rockwell hardness more that 50 and one no more than 75?
c) Within what limits would you expect. the Rockwell hardness to lie, with prob-
ability .98?
Transcribed Image Text:Problem 1. The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of pene tration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. (Rockwell hardness is measured on a continuous scale.) a) If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness? b) If two alloys are randomly selected, which is the probability that one will have Rockwell hardness more that 50 and one no more than 75? c) Within what limits would you expect. the Rockwell hardness to lie, with prob- ability .98?
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman