Question

a process makes parts eith s criticsl dimension that can be modeled as a normsl distribution with mean 39.98 and standard deviation 0.08 inches. if the specification for that dimension is 39.8 to 40.2 inches what percentage of output would be defective

Answer 1

Let x be the dimension of the part .

A part is defective if x<39.8 and x >40.2

In normal distribution ,

z=x-mean/std dev

Given : mean=39.98 and std dev =0.08

P(x=39.8)=P(z=39.8-39.98/0.08) =P(z=-2.5)=0.012224

P(x=40.2)=P(x=40.2-39.98/0.08)=P(z=2.75)=0.99702

P(x>40.2)=1-P(x=40.2)=1-0.99702=0.00298

Probability that the dimension is not within the dimension =P(x<39.8)+P(x>40.2)

=0.012224+0.00298

=0.015204

=1.52 %