Mary and john are competing in a food competition. their dish is graded on the following categories each worth 18 points: taste, presentation, and addressing the challenge. taste is worth 60% of their final score; presentation is 25%, and addressing the challenge is 15%. whoever has the largest final score wins $50,000.
a. what is the largest score possible?
b. suppose maryreceived15 points for taste, 9 points for presentation, and 14 points for addressing the challenge. further suppose john received18 points for taste, 7 points for presentation, and 13 points for addressing the challenge. who won?

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.