Question 4.32: If a fair coin is tossed 100 times, use the normal curve to ...

This situation is illustrated in Figure 4.20.Let X be the number of heads obtained. Then X~ Bin (100, 0.5). Substituting n = 100 and p = 0.5 into Equation (4.35), we obtain the normal approximation X ~ N(50, 25). Since the endpoints 45 and 55 are to be included, we should compute the area under the normal curve between 44.5 and 55.5. The z-scores for 44.5 and 55.5 are

X \sim N(n p, n p(1-p)) \quad \text{approximately}        (4.35)

z=\frac{44.5-50}{5}=-1.1, \qquad z=\frac{55.5-50}{5}=1.1

From the z table we find that the probability is 0.7286. See Figure 4.22.