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

Answer:

$\sigma=0.000215$

Step-by-step explanation:

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

$z=\frac{x-\mu}{\sigma}$

$\sigma = \frac{x-\mu}{z}$

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

$\sigma = \frac{0.0026-0.002}{2.78}=\frac{0.0006}{2.78}= 0.000215$