Question 4.33: If a fair coin is tossed 100 times, use the normal curve to ...

This situation is illustrated in Figure 4.21. Let X be the number of heads obtained. As in Example 4.32, X ∼ Bin(100, 0.5), and the normal approximation is X∼ N(50, 25). Since the endpoints 45 and 55 are to be excluded, we should compute the area under the normal curve between 45.5 and 54.5. The z-scores for 45.5 and 54.5 are

z=\frac{45.5-50}{5}=-0.9, \qquad z=\frac{54.5-50}{5}=0.9

From the z table we find that the probability is 0.6318. See Figure 4.23.