Question

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inch and a standard deviation of 0.0004 inch. What is the probability that a diameter is between 0.0014 and 0.0026 inches

Answer 1

Answer:

$P(0.0014 < x < 0.0026) = 0.86639$

Step-by-step explanation:

Given

$\mu = 0.002$

$\sigma = 0.0004$

Required

$P(0.0014 < x < 0.0026)$

First, calculate the z score

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

For x = 0.0014

$z = \frac{0.0014 - 0.002}{0.0004}$

$z = \frac{-0.0006}{0.0004}$

$z = -1.5$

For x = 0.0026

$z = \frac{0.0026 - 0.002}{0.0004}$

$z = \frac{0.0006}{0.0004}$

$z = 1.5$

So, we have:

$P(0.0014 < x < 0.0026) = P(-1.5<z<1.5)$

From z probability table, we have:

$P(-1.5<z<1.5) = 0.86639$

Hence:

$P(0.0014 < x < 0.0026) = 0.86639$