EXAMPLE 5.14 Using the Normal Approximation

CASE 5.1 As described in Case 5.1 (page 247), a quality engineer inspects an SRS of 150 switches from a large shipment of which 8% fail to meet specifications. The count of nonconforming switches in the sample were thus assumed to be the distribution. In Example 5.10 (page 254), we found and .

The Normal approximation for the probability of no more than 10 nonconforming switches is the area to the left of under the Normal curve. Using Table A,

In Example 5.5 (pages 247–248), we found that software tells us that the actual binomial probability that there is no more than 10 nonconforming switches in the sample is . The Normal approximation is only roughly accurate. Because , this combination of and is close to the border of the values for which we are willing to use the approximation.