Question

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inch. Suppose that the specifications require the dot diameter to be between 0.0014 and 0.0026 inch. If the probability that a dot meets specifications is to be 0.9973, what standard deviation is needed

Answer 1

`\sigma=0.000215\\`

Explanation:

`\mu=0.002 inches\\P(0.0014<x<0.0026)=0.9973\\`

`z=(x-\mu)/(\sigma)`

`\sigma = (x-\mu)/(z)`

We obtain z from the normal distribution tables:

As P (0.0014<x<0.0026)=0.9973), we search 0.9973 on the table, to obtain

z= 2.78

`\sigma = (0.0026-0.002)/(2.78)=(0.0006)/(2.78)= 0.000215`