Bill and matt are discussing their children. bill tells matt that he has 3 kids, and the product of their ages is 72. he also tells him the sum of the ages of his kids. matt says there is still not enough information to correctly guess the ages of bill's kids. finally, bill says, my youngest child's name is joy. matt can then correctly guess. what are the ages?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.