A college survey was taken to determine where students study. Of 113 students surveyed, 71 studied in the library, 63 studied in the student lounge, 27 studied in
both the library and the student lounge.
Of those interviewed how many did not study in either the library or the student lounge?

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.