EXAMPLE 5.26

Compare the Normal approximation with the exact calculation. Let’s compare the Normal approximation for the calculation of Example 5.24 with the exact calculation from software. We want to calculate when the sample size is and the population proportion is . Example 5.25 shows that

Act as if were Normal with mean 0.6 and standard deviation 0.0098. The approximate probability, as illustrated in Figure 5.18, is

≐ P(Z ≥ −2.04) = 0.9793

That is, about 98% of all samples have a sample proportion that is at least 0.58. Because the sample was large, this Normal approximation is quite accurate. It misses the software value 0.9802 by only 0.0009.