Each side of the square below is 8 inches.

A triangle inside of a square. The top of the triangle divides a side of the square into 2 equal parts of 4 inches. The triangle is shaded and the area to the right of the triangle is shaded.

What is the probability that a point chosen at random in the square is in the blue region?

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.