Question 4.32: If a fair coin is tossed 100 times, use the normal curve to ......
If a fair coin is tossed 100 times, use the normal curve to approximate the probability that the number of heads is between 45 and 55 inclusive.
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),
If X ∼ Bin(n, p), and if np > 10 and n(1 − p) > 10, then
X ∼ N(np, np(1 − p)) approximately (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
z = \frac{44.5\ −\ 50}{5} = −1.1, z = \frac{55.5\ −\ 50}{5} = 1.1
From the z table we find that the probability is 0.7286. See Figure 4.22.
