Question

For a population with u= 100 and o=15, find the X value that corresponds to each of the followingZ-scores:(a) Z= -0.25, X=(b)Z= -1.50, X=(c) Z= 0.50, X=(d) Z= 2.00, X=

Answer 1

The z-score of a value is given by the following formula:

$z=\frac{x-\mu}{\sigma}$

Where mu represents the mean and sigma the standard deviation. We can rewrite this formula with the actual value as function of the z-score:

$z=\frac{x-\mu}{\sigma}\implies x=\mu+\sigma z$

Then, using this formula in our problem, we have the following results:

$\begin{gathered} a)\quad x=100+15(-0.25)=96.25 \\ b)\quad x=100+15(-1.50)=77.5 \\ c)\quad x=100+15(0.50)=107.5 \\ d)\quad x=100+15(2.00)=130.0 \end{gathered}$