Question

Find the sum with a $z$–score of $0.5$.

Short answer

The sum with a$z-$score of$0.5$is$\sum X=3903.5$.

Step-by-step solution

Given Information

A sample size $\left(n\right)=100$.

The mean of population $\left({\mu }_X\right)=39.01$.

$z=0.5$.

A standard deviation $\left({\sigma }_X\right)=0.5$.

Exlpanation

To find the sum with a $z-$score of$0.5$:

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

Calculating, we have:

$\sum X=100\times 39.01+0.5\times \sqrt{100}\times 0.5$

$\sum X=3903.5$