and architect is trying to figure out how to lay out a kitchen, a family room, and a living room in the new house. he wants 1/2 of the floor to be the family room. once that is marked off, the architect wants 2/3 of the remaining space to be the kitchen and the rest to be the living room. what is the fraction of the whole that the kitchen will take up?

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.