Tags are placed to the left leg and right leg of a bear in a forest. Let A1 be the event that the left leg tag is lost and A2 the event that the right leg tag is lost. Suppose these two events are independent and P(A1)=P(A2)=.4. Find the probability that exactly one tag is lost, given that at least one tag is lost.

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.