Problem
A large artificial insemination stud has just purchased a promising Red Angus bull. Management is concerned, however, that the bull might be a carrier of osteopetrosis (marble bone disease), a recessive lethal condition. Assume that there is no DNA test for the recessive allele. (Note: There has been a DNA test since 2011) Five percent of all cows are thought to be carriers of the osteopetrosis allele. A.I. matings to randomly selected cows have already produced 87 normal calves and no osteopetrosis calves. What is management's level of confidence that the bull is not a carrier of the osteopetrosis allele?