PO) Binomial f(x) Normal 0.2 Binomial + Normal 0.1 0.0 4 0 10 X (b1 a. Binomial with P = 0.50 and 1 = 100, and Normal with = 50 and a = 5 b. Binomial with P = 0.20 and = 25, and Normal with x = 5 and 0 = 2 and the normal distribution does not provide a good approximation for the binomial dis- tribution. Evidence such as that contained in Figure 5.24 has provided the rationale for widespread application of the normal approximation for the binomial. We will now pro- ceed to develop the procedure for its application S Normal Distribution Approximation for linomial Distribution 201 51 Z By using the mean and the variance from the binomial distribution, we find that it the number of trials is large such that P(1-P) > 5 then the distribution of the random variable X EX X- V Var VIPP is approximately a standard normal distribution. This result is very important because it allows us to find, for large n, the probability that the number of successes lies in a given range. If we want to determine the probability that the number of successes will be between a and b, inclusive, we have VP1-P) n X- = VP VHP - P - HP 2 Vol 1 Vull - With large, Z is well approximated by the standard normal, and we can find the prob- ability using the methods from Section 53 Example 5.8 Customer Visits Generated From Web Page Contacts (Normal Probabilities) Mary David makes the initial telephone contact with customers who have responded to an advertisement on her company's Web page in an effort to assess whether a follow- up visit to their homes is likely to be worthwhile. Her experience suggests that 40% of the initial contacts lead to follow-up visits. If she has 100 Web page contacts, what is the probability that between 45 and 50 home visits will result