EXAMPLE 5.27

Using the Normal approximation. The audit described in Example 5.19 examined an SRS of 150 sales records for compliance with sales tax laws. In fact, 8% of all the company’s sales records have an incorrect sales tax classification. The count X of bad records in the sample has approximately the distribution.

According to the Normal approximation to the binomial distributions, the count X is approximately Normal with mean and standard deviation

The Normal approximation for the probability of no more than 10 misclassified records is the area to the left of X = 10 under the Normal curve. Using Table A,

≐ P(Z ≤ −0.60) = 0.2743

Software tells us that the actual binomial probability that no more than 10 of the records in the sample are misclassified is . The Normal approximation is only roughly accurate. Because , this combination of n and p is close to the border of the values for which we are willing to use the approximation.