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 ΣX is 42?

Short answer

The sample size is used to calculate the number of individuals in a particular area in statistical terms.

Step-by-step solution

Given information

The mean of the unknown distribution is$25$and the standard deviation is six and the standard deviation of$\sum X$is$42$. The formula for the standard deviation is;

$\sum X=\left(\sqrt{n}\right)\left({\sigma }_X\right)$

The sample size is;

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

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

$\sqrt{n}=7$

$n=49$

Final answer

The sample size for the given distribution is$49$.