The Rockwell hardness of a metal is determined by impressing a hardened point in

Question

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) What is the probability that the Rockwell hardness of a randomly selected alloy is greater than 77?

b) What Rockwell hardness is the 95% percentile?

c) Using the result in part a), if five alloys are randomly selected, what is the probability that excatly one of them has a greater Rockwell hardness than 77 inches?

Explanation / Answer

mean 70 and

standard deviation 3

a) z = (77 - 70)/3

z = 2.33

P = 0.0099

b) z for 95% one side = 1.645

(x - 70)/3 = 1.645

x = 74.935

c) p = 0.0099

n = 5

P(X = 1) = 5C1 * 0.0099^1 * 0.9901^4

P = 0.0476

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