The Bungling Brothers Circus is in town and you are part of the crew that is setting up its enormous tent. The center pole that holds up the tent is 74 feet tall. To keep it upright, a support cable needs to be
attached to the top of the pole so that the cable forms a 55 degree angle with the ground.

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.