Question

A researcher of a cardboard manufacturing company would like to know the estimated thickness of the cardboard a machine produces How many cardboards should he measure if he wants to be 99% confident that the estimate is accurate to 1 mm. Study shows that the standard deviation is 3mm

Answer 1

The formula for error:

$E=z\cdot \cfrac{\sigma}{\sqrt{n}}.$

Here

$E\ -$ the error, $E=1$ mm;

$z\ -$ z-score, for 99% confidence level $z=2.576$ ;

$\sigma -$ the he standard deviation, $\sigma =$ 3 mm;

$n\ -$ the sought sample size.

So,

$n=\begin{pmatrix} \cfrac{z\cdot\sigma}{E} \end{pmatrix}^2=\begin{pmatrix} \cfrac{2.576\cdot3}{1} \end{pmatrix}^2=59.7.$

The minimum amount of cardboards the researcher should measure is 60.