Question

The inside diameter of metal washers produced by a company are normally distributed with a mean of .5 inches and a standdrd deviation of .01 inches. Of all washers produced .8% of the washers are rejected because they are too small for a bolt used to test them. What is the diameter of the bolt used for the test?

Answer 1

Given:
μ=0.5"
σ=0.01"
Rejection rate = 0.8% = 0.008
rejection criterion = z<Z
X=μ+Zσ
=0.5+0.01Z

From normal distribution tables
P(Z<-2.409)=0.008
so
X=0.5-0.01*2.409
=0.4758

Ans: washers with diameters less than 0.476 are rejected.