Apharmaceutical company receives large shipments of aspirin tablets. the acceptance sampling plan is to randomly select and test 58 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. if one shipment of 6000 aspirin tablets actually has a 2% rate of defects, what is the probability that this whole shipment will be accepted/

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.