Question

A study reports that the mean lifetime of a certain type of tire is 39500 miles with a standard deviation of 986 miles.

Random samples of size 150 are taken from this type of tire. What would be the standard deviation of the distribution of the sample means? Round to two decimal places, if necessary.

Answer 1

Solution

$\small \\\mathbf{given:}\;Population\;mean\;(\mu)=39500,\;Population\;standard\;deviation\;(\sigma)=986,\;Sample\;size\:(n)=150$

$\small The \;standard\; deviation\;of\; the\; distribution\; of \;the\; sample \;means\;(\sigma_{\bar x})=\frac{\sigma }{\sqrt{n}}$

986 03 = 150

0 = 80.50656288

Round to two decimal places.

$\small \mathbf{\sigma_{\bar x}={\color{Red} 80.51}}$