5. There are 5 civil cases waiting for trial in a paricular state. In each of the 5 cases the defendant is a corporation, the null-hypothesis is that the corporation did not discriminate against women, and the alternative hypothesis is that the corporation discriminated against women. The court will base its decision in all 5 cases on a t test with 1% significance level. Suppose that none of the 5 corporation discriminated against women. (a) What is the probability that the court will make the correct decision in all 5 cases? (10 pts.) (b) What is the probability that the court is going to make 1 erroneous and 4 correct decisions? (10 pts.) (c) Suppose that we are particularly interested in corporation A, which is one of the 5 corporations waiting for trial. What is the probability that corporation A will be unjustly penalized, but in the other 4 cases the court will make the correct decision? (10 pts.) (d) What is the probability that the court will make at least 1 erroneous decision in the 5 cases? (10 pts.)