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 7 ounces.

The process standard deviation is 0.1, and the process control is set at plus or minus 2 standard deviations. Units with weights less than 6.8 or greater than 7.2 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?

Answer 1

Answer:

0.05 = 5% probability of a defect.

Step-by-step 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 = 7

Standard deviation = 0.1

Units with weights less than 6.8 or greater than 7.2 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?

6.8 = 7 - 2*0.1

So 6.8 is two standard deviations below the mean

7.2 = 7 + 2*0.1

So 7.2 is two standard deviations above the mean.

By the Empirical Rule, 95% of the measures are within 2 standard deviations of the mean, that is, within 6.8 and 7.2. The other 5% is more than 2 standard deviations from the mean, that is below 6.8 or greater than 7.2.

So, there is a 0.05 = 5% probability of a defect.