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 9 ounces. The process standard deviation is 0.15, and the process control is set at plus or minus 1 standard deviation. Units with weights less than 8.85 or greater than 9.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)

Answer 1

`1-P(8.85 < X < 9.15)=0.3173`

Explanation:

We need to first calculate the probability that a unit between the weight of 8.85 and 9.15 ounces is NOT a defect, then subtract it from 1.

It just so happens that 8.85 and 9.15 are both 1 standard deviation from the mean of 9, so by the Empirical Rule,
`P(8.85 < X < 9.15)=0.6827`.

Thus, the probability of a unit being a defect is
`1-P(8.85 < X < 9.15)=1-0.6827=0.3173`