We need to find the value of X in each case.
The problem tells us to use the formula:
[tex]X=\mu+Z\sigma[/tex]
First, let's identify what each of the terms in the formula stands for. We have:
[tex]\begin{gathered} X:\text{ the value we need to find} \\ \\ \mu:\text{ the mean of the distribution } \\ \mu=9 \\ \\ Z:\text{ the z-score specific to each value of X} \\ \\ \sigma:\text{ the standard deviation of the distribution} \\ \sigma=2 \end{gathered}[/tex]
Now, we need to replace Z with the value given in each item, replace μ with 9 and replace σ with 2.
By doing so, we obtain:
A) Z = -0.5
[tex]\begin{gathered} X=\mu+Z\sigma \\ \\ X=9+(-0.5)2 \\ \\ X=9-0.5\times2 \\ \\ X=9-1 \\ \\ X=8 \end{gathered}[/tex]
B) Z = 0
[tex]\begin{gathered} X=\mu+Z\sigma \\ \\ X=9+0\times2 \\ \\ X=9+0 \\ \\ X=9 \end{gathered}[/tex]
C) Z = 1.96
[tex]\begin{gathered} X=\mu+Z\sigma \\ \\ X=9+1.96\times2 \\ \\ X=9+3.92 \\ \\ X=12.92 \end{gathered}[/tex]
Answer
A) X = 8
B) X = 9
C) X = 12.92
