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 71 and standard deviation 3.

If the acceptable range is 67 and 75 and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten? (Round your answer to two decimal places.)

Explanation / Answer

Mean is 71 and s is 3. z is calculated as (x-mean)/s

P(67<x<75)=P((67-71)/3<z<(75-71)/3)=P(-1.33<z<1.33)=2*P(z<1.33)-1

from normal distribution table we get 2*0.9082-1=0.8164

out of 10 it is 10*0.8164 =8.17

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