A engineer conjectures that the population mean of a certain component parts is 5.0 millimeters. An experiment is conducted in which 100 parts produced by the process are selected randomly and the diameter measured on each.
It is known that the population standard deviation σ = 0.1. The experiment indicates a sample average diameter X = 5.027 millimeters.
Does this sample information appear to support or refute the engineer’s conjecture?
The solution goes by this
here is what bothers me, why is that, he considered the area P(z>2.7). From my point of view, it should be set up like this P(z<2.7) (since we are finding the probability that the length should be between 0 and 0.027 mm. Then it yields 0.99 which means, 99% of the time, it falls with -0.027 - 0 - 0.027 and should support the engineers conjecture. Thanks
Please illuminate me if Im wrong