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?

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter29: Tolerance, Clearance, And Interference
Section: Chapter Questions
Problem 16A: Spacers are manufactured to the mean dimension and tolerance shown in Figure 29-12. An inspector...
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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?
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