When a basketball player makes a trip to the free throw line, he takes two consecutive shots. It is often wondered whether these two shots are independent or dependent: does the probability of making the second free throw depend
on whether a player makes the first free throw?
After analyzing data for Lebron James, statisticians determined that his first and second free throws are entirely
independent events. The frequency table below shows the data that analysts used to determine this independence.

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.