Because of the unique line postulate, we can draw unique
line segment PM. Using the definition of reflection, PM can
be reflected over line l. By the definition of reflection, point P
is the image of itself and point N is the image of
Because reflections preserve length, PM = PN.
point M
point Q
segment PM
segment QM

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.