A chemical company makes two brands of antifreeze the first brand is 55% pure anti-freeze in the second brain is 80% pure anti-freeze in order to obtain 50 gallons of a mixture that contains 70% pure anti-freeze how many gallons of each brand of antifreeze must be used

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.