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

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

Explanation:

Given

`\mu = 0.002`

`\sigma = 0.0004`

Required

`P(0.0014 < x < 0.0026)`

First, calculate the z score

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

For x = 0.0014

`z = (0.0014 - 0.002)/(0.0004)`

`z = (-0.0006)/(0.0004)`

`z = -1.5`

For x = 0.0026

`z = (0.0026 - 0.002)/(0.0004)`

`z = (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`