1. A local business kept track of their sales each month for two years. They used this data to create a sales model for their business. The model is y = -0.25x^2 +
6x + 40 hundred dollars per month.
i. Determine when the maximum sales value occurs
ii. Determine the actual maximum sales.
iii. Also, use a graphing calculator to determine when the sales value would be zero
in context of the problem.

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.