An automatic machine is used to fill boxes with soap powder. Specifications requ

Question

An automatic machine is used to fill boxes with soap powder. Specifications require that the boxes weigh between 11.8 and 12.2 ounces. The only data available about machine performance concern the average content of groups of nine boxes.It is known that the average content is 11.9 ounces with a standard deviation of 0.05 ounce. What fraction of the boxes produced is defective? Where should the mean be located in order to minimize this fraction defective? Assume the weight is normally distributed.

Explanation / Answer

First of all, figure out how many standard deviations below andabove the mean you are allowed to be. (11.8-11.9)/.05 = - 2standard deviations,                            (12.2 - 11.9)/.05 = 4 standard deviations If X is above 2 standard deviations below the mean, and below 4standard deviations above the mean, it can be rewritten as P(-2

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