A marketing firm tracks data on grocery store visits. In one study, it finds that the probability that a shopper buys bread during a visit to the grocery store is
0.60, and the probability that a shopper buys cheese is 0.25.
Event A = A shopper buys bread
Event B = A shopper buys cheese.
A and B are independent events if
A. the probability of buying bread or cheese is 0.15
B. the probability of buying bread or cheese is 0.85
C. the probability of buying bread and cheese is 0
D. the probability of buying bread and cheese is 0.15

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.