Using the Empirical Rule and Chebyshev’s Theorem An experiment is designed to test the effectiveness of the MicroSort method of gender selection, and 100 couples try to have baby girls using the MicroSort method. In an example included in this section, the range rule of thumb was used to conclude that among 100 births, the number of girls should usually fall between 40 and 60.

a. The empirical rule (see Section 2-5) applies to distributions that are bell-shaped. Is the binomial probability distribution for this experiment (approximately) bellshaped? How do you know?

b. Assuming that the distribution is bell-shaped, how likely is it that the number of girls will fall between 40 and 60 (according to the empirical rule)?

c. Assuming that the distribution is bell-shaped, how likely is it that the number of girls will fall between 35 and 65 (according to the empirical rule)?

d. Using Chebyshev’s theorem, what do we conclude about the likelihood that the number of girls will fall between 40 and 60?