Question

An unknown distribution has a mean of $25$ and a standard deviation of six. Let $X$ = one object from this distribution. What is the sample size if the standard deviation of $\Sigma X$ is $42$?

Short answer

The sample size is$49$.

Step-by-step solution

Given Information

An unknown distribution has a mean of $25$ and a standard deviation of six.

Explanation

The sample size if the standard deviation of $\Sigma X=\left(\sqrt{n}\right)\left({\sigma }_x\right)$

Therefore, the sample size is:

$42=\sqrt{n}\times 6$

$\sqrt{n}=\frac{42}{6}$

role="math" localid="1648890741186" $\sqrt{n}=7$

$n=49$

Therefore, the sample size is$49$