Simon wants to build a rectangular pen in his backyard for his rabbit, Smiley. Simon has 18m of wire mesh for a fence to enclose the pen. Simon wants the greatest possible area for the penvwhich is rectangular in shape. Help him to solve his problem.

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.