During the quarantine, the Jones family installed a rectangular pool in their backyard that was 10 feet wide and 15 feet long. The Martin family, not to be outdone, wanted to install a circular pool in their backyard but wanted to make sure that their pool covered a larger area of their yard than the Jones’ pool covered of their backyard. What should the diameter of the Martin family’s pool be to ensure that it is larger than the Jones’ family (round to the nearest foot)?

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.