Question

Find the sum that is $1.5$ standard deviations below the mean of the sums.

Short answer

The sum is$\sum X=7424.5577$.

Step-by-step solution

Given Information

A sample size $\left(n\right)=95$.

The mean of population $\left({\mu }_X\right)=80$.

$z=1.5$

A standard deviation $\left({\sigma }_X\right)=12$.

Explanation

To find the sum that is$1.5$standard deviation below the mean of the sums:

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

Calculating, we have:

$\sum X=95\times 80-1.5\times \sqrt{95}\times 12$

$\sum X=7424.5577$