Question

How many parts should be sampled in order to estimate the population mean to within 0.1 millimeter (mm) with 95% confidence? Previous studies of this machine have indicated that the standard deviation of lengths produced by the stamping operation is about 1.8 mm.

Answer 1

At least 1245 parts should be sampled.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.95)/(2) = 0.025`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.025 = 0.975`, so
`z = 1.96`

Now, find the margin of error M as such

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

How many parts should be sampled in order to estimate the population mean to within 0.1 millimeter (mm) with 95% confidence?

This is at least n parts, in which n is found when
`M = 0.1, \sigma = 1.8`

`M = z*(\sigma)/(√(n))`

`0.1 = 1.96*(1.8)/(√(n))`

`0.1√(n) = 1.96*1.8`

`√(n) = (1.96*1.8)/(0.1)`

`(√(n))^(2) = ((1.96*1.8)/(0.1))^(2)`

`n = 1244.67`

Rouding up

At least 1245 parts should be sampled.