Baseball: The bases on a baseball
diamond form a square 90 ft on a
side. The pitcher's plate is 60 ft
6 in. from the back corner of
home plate.

a. About how far is the pitcher's
plate from second base?

b. A line drive is 10 ft high when it
passes over the third baseman,
who is 100 ft from home plate.
At what angle did the ball leave
the bat? (Assume the ball is 4 ft
above the ground when it is hit.)

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.