Question

Z = x − ms for the variable m using z = −3, s = 16.8, and x =29.4

Answer 1

• mean = 79.8

,

• mean = 14.4

1) Solving for m, plugging it for the z-score formula we have:

`\begin{gathered} Z=(X-m)/(s) \\ -3\text{ =}(29.4-m)/(16.8)\text{ x16.8} \\ -50.4\text{ =29.4-m} \\ m=50.4+29.4 \\ m=79.8 \end{gathered}`

We can state then the mean is 79.8, the s stands for Sample Deviation. Note that we multiplied both sides by 16.8 and added 50.4 to both sides

2) The second Z-score formula presents the following data:

`\begin{gathered} Z=(X-m)/(s) \\ 3=(24.9-m)/(3.5)\text{ x 3.5} \\ 10.5=24.9-m \\ m=24.9-10.5 \\ m=14.4 \end{gathered}`

The difference for that is the Standard Deviation (3) and the Z-score.

3) Hence, the answer is

0. mean = 79.8

,

1. mean = 14.4