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Heated-treated parts are specified to have a hardness of at least 45 (lower specification limit). Any...

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.

Answer the following and provide a sketch of the distribution used for the setup of your calculations.

a. What is the probability that a part is below the minimum specified hardness?

b. What would the lower specifications have to be changed to so that only 1% of the parts would be below specifications?

math   Statistics-And-Probability   
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