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2. A certain mechanical component is to be manufactured with a diameter of 3 centime-

ters. The manufacturing process produces components whose diameters are normally

distributed with mean value μ = 3 and standard deviation is 0.02 cm.

(a) What percentage of components will have a diameter greater than 3.045 cm?

(b) What percentage of components with have a diameter less than 2.95 cm?

(c) If the manufacturer discards any component with a diameter that differs from 3 cm

by more than 0.03 cm (in either direction), then what percentage of components

will be discarded?