Joe is standing at a Point P of a parking lot that is in the shape of a right triangle as shown in the diagram. There is a fence along the longest side of the lot. Joe's distance to the fence is 15 meters. There is a sign on the fence at Point C. The distance from A to C is 8 meters. If the width of the lot, segment a, p, is 17 meters, then how long is the fence, segment a, b?'

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.