Question

Automated manufacturing operations are quite precise but still vary, often with distributions that are close to Normal. The width in inches of slots cut by a milling machine follows approximately the N(0.8750,0.0014)

distribution. The specifications allow slot widths between 0.8725 and 0.8775 inch.

What proportion (±

0.001) of slots meet these specifications (use software)?

Answer 1

Since the distribution is normal with mean=0.8750 and standard deviation= 0.0014 so we use Z score for proportion calculation hence Z at 0.8725

and Z at 0.8775

Hence P(0.8725<X<0.8775) =P(-1.79<Z<1.79) is calculated using Z table shown below as

=0.9633- 0.0367

=0.8963