Question

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. 1. The process standard deviation is 0.15 and the process control is set at plus or minus on standard deviation, so units with weights less than 9.85 oz or greater than 10.15 oz will be classified as defects. Find the probability of a defect and the expected number of defects for a 1000-unit production run.

Answer 1

32% probability of a defect.

The expected number of defects for a 1000-unit production run is 320.

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 10

Standard deviation = 0.15.

Probability of a defect

Weights less than 9.85 oz or greater than 10.15 oz will be classified as defects.

9.85 = 10 - 0.15

10.15 = 10 + 0.15

By the Empirical Rule, 68% of weights are between 9.85 and 10.15, that is, within the limits. 32% are not within the limits.

So there is a 32% probability of a defect.

Expected number of defects for a 1000-unit production run.

E(X) = 0.32*1000 = 320

The expected number of defects for a 1000-unit production run is 320.