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The hardness of a metal is determined by forcing a hardened point into the surface and...

  1. The hardness of a metal is determined by forcing a hardened point into the surface and then measuring the depth of penetration of the point. Suppose the hardness of a particular metal is normally distributed with mean 70 and standard deviation 3.
  1. If a sample is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen sample has an acceptable hardness? (12 pts)
  2. If the acceptable range of hardness is (70-c, 70+c), for what value of c would 95% of all specimens have acceptable hardness? (13 pts)
Math   Statistics-And-Probability   
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