Answer to Question #258873 in Statistics and Probability for THIRDY VARGAS

Question

1.       The mean inside diameter of a sample of 200 washers produced by a machine is 0.502 inch and the standard deviation is 0.005 inch. The purpose for which these washers are intended allows a maximum tolerance in the diameter of 0.496 to 0.508 inch, otherwise, the washers are considered defective. Determine the percentage of defective washers produced by the machine, assuming that the diameters are normally distributed.

Answer 1

$$P(0.496<X<0.508)$$

$$=P(X<0.508)-P(X\leq0.496)$$

$$=P(Z<\dfrac{0.508-0.502}{0.005/\sqrt{200}})$$

$$-P(Z\leq\dfrac{0.496-0.502}{0.005/\sqrt{200}})$$

$$=P(Z<16.97056)-P(Z\leq-16.97056)$$

$$\approx1-0=1$$

$$1-P(0.496<X<0.508)=1-1=0$$

The percentage of defective washers produced by the machine is $0\%.$