A synthetic female hormone (DES) has been used to fatten livestock. If this substance appears in the meat, it affects the sexual maturity of young animals eating the meat. Biological assays can be used to test for the presence of DES in meat. Young female rats are fed the suspected meat, and if they mature earlier than expected, it is probably because of DES in the meat. Suppose for a given strain of rat that time until sexual maturity in the females follows an essentially normal distribution with a mean of 90 days and a variance of 144.

a. What is the probability that a randomly selected female rat will reach sexual maturity before 90 days? Before 86 days?

b. What is the probability that the average time until sexual maturity of nine female rats will be less than 90 days? Less than 86 days?

c. A random sample of nine female rats is fed a diet including meat suspected of containing DES.

i. What are the most logical null and alternative hypotheses?

ii. If a = 0.05, which values of the sample average will lead to the rejection of the null hypothesis?

iii. Suppose for female rats on a diet containing DES sexual maturity follows an N(86, 144) distribution; what is the probability of making a Type II error?