Heated-treated parts are specified to have a hardness of at least 45 (lower spec

Question

Heated-treated parts are specified to have a hardness of at least 45 (lower specification limit). Any parts that are below 45 are too soft and have to be heat treated again at great expense. The hardness of heat-treated parts actually produced follows a normal distribution with a mean of 48.5 with a standard deviation of 2. (Note: sketch of the distribution helps the set up your calculation).

To calculate the probability that a part is below the minimum specified hardness, calculate the z value of minimum specification.

Explanation / Answer

Z = ( X - mean)/SD

   = (45 - 48.5)/2

   = -1.75

P(Z < -1.75) = 0.0401

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