10.104 The guidelines to ensure the sampling distribution of p1  p2 is normal include several conditions about the size of several values. The two binomial distributions B(100, 0.3) and B(100, 0.4)

satisfy all of those guidelines.

a. Verify that B(100, 0.3) and B(100, 0.4) satisfy all guidelines.

b. Use a computer to randomly generate 200 random samples from each of the binomial populations.

Find the observed proportion for each sample and the value of the 200 differences between two proportions.

c. Describe the observed sampling distribution using both graphic and numerical statistics.

d. Does the empirical sampling distribution appear to have an approximately normal distribution?

Explain.