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 polnt. Suppose the Rockwell hardness of a particular alloy is normally dlstributed with mean 70 and standard deviation 3. (a) If a specimen is acceptable only if its hardness is between 66 and 74, what is the probability that a randomly chosen specimen has an acceptable hardness? (Round your answer to four decimal places.) 0.8164 (b) If the acceptable range of hardness is (70-c, 70 + c), for what value of c would 95% of all specimens have acceptable hardness? (Round your answer to two decimal places.) 5.88 (c) If the acceptable range is as in part (a) 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.) 0.89973 Xspecimens

Explanation / Answer

The probability of one specimen being in the acceptable range is 0.8164 from part -a.

Hence, p = 0.8164

Also, n = 10

E( Specimens falling in the range) = np = 0.8164*10 = 8.164 = 8.16

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