Two hundred and twenty-three students were asked if their favorite summer vacation destination was in North Carolina, Georgia, or South Carolina. Of these students, 121 were girls, 75 students chose South Carolina, and 55 chose Georgia. Of the boys, 59 chose North Carolina while 25 of the boys chose Georgia. Determine the relative frequency of a girl who chose to go to North Carolina. Explain your reasoning.

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.