In Chapter 6, you will see that the normal distribution can sometimes be used to approximate the

Question:

In Chapter 6, you will see that the normal can sometimes be used to approximate the binomial This exercise is designed to illustrate how good the normal approximation to the binomial can be.
a. Consider a binomial with n = 200 and p = 0.5.Calculate P(x ≤ 100).
b. What is the mean and standard deviation for the you used in part a?
c. Using a normal with the same mean and standard deviation you calculated in part b, calculate P(x ≤ 100).
d. Now calculate P(x ≤ 100.5) for the normal The extra 0.5 is added to provide a “continuity correction factor.”It compensates for the fact that the normal is continuous (so P(x ≤ 100) = P(x < 100), for example), and the binomial is not (P(x ≤ 100) ≠ P(x < 100)).How close are the binomial and normal probabilities now? Distribution
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