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 68 and standard deviation 3. (a) if a specimen is acceptable only if its hardness is between 65 and 71, what is the probability that a randomly chosen specimen has an acceptable hardness? (round your answer to four decimal places.) 0.6826 correct: your answer is correct.

0.6826

Step-by-step explanation:

Since it's a normal distribution

z = (x - m)/s where

m = mean = 68

s = standard deviation = 3

z = standard normal variable

x = values of hardness of the specimen

a) we are looking for P( 65 lesser than/equal to x lesser than/ equal to 71

For x= 65,

z = (65-68)/3 = -3/3 = -1

For x= 71

z = (71 -68)/3 = 3/3 =1

Looking at the normal distribution table,

For area covered by

(z = -1 to z= 1) = 0.1587

For area covered by

(z = 0 to z=1) = 0.8413

P( 65 lesser than/equal to x lesser than/ equal to 71) = 0.8413 -0.1587

= 0.6826

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step-by-step explanation: