Question

A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.600 in. A bearing is acceptable if its diameter is within 0.004 in. of this target value. Suppose, however, that the setting has changed during the course of production, so that the distribution of the diameters produced is well approximated by a normal distribution with mean 0.599 in. and standard deviation 0.002 in. What percentage of the bearings produced will not be acceptable? (Round your answer to two decimal places.)

Answer 1

Given that X follows a Normal distribution with Mean-μ-0.599 SD : ơ :0.002 Note thatz-(x-u)/ơ :(x-0.599/0.002 (Eq.1) When x 0.596, from (Eq.1),z--1.5 follows standard Normal. When x 0.604, from (Eq.1), z 2.5 P(0.596-X < 0.604)-P(-1.5-z-2.5): P(Z < 2.5)-P(Z <-1.5-0.9938-0.0668-0.927 P(not acceptable)-1-0.927-0.073 7.30 %