use ) 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? ) What is the probability that a randomly chosen specimen has a hardness over 80? ) If the acceptable range of hardness is (70c, 70+ c), for what value of c would 95% of all specimens have acceptable hardness?

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Use Appendix Table A.3 to answer the following. 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 penetration of the
point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3.
(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) What is the probability that a randomly chosen specimen has a hardness over 80?
(c) If the acceptable range of hardness is (70c, 70+ c), for what value of c would 95% of all specimens have acceptable
hardness?
Transcribed Image Text:Use Appendix Table A.3 to answer the following. 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 penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. (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) What is the probability that a randomly chosen specimen has a hardness over 80? (c) If the acceptable range of hardness is (70c, 70+ c), for what value of c would 95% of all specimens have acceptable hardness?
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