In order to calculate the salary for a z-score of 2, we can use the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where μ is the mean and σ is the standard deviation.
So, for z = 2, μ = 54134 and σ = 10320, we have:
[tex]\begin{gathered} 2=\frac{x-54134}{10320} \\ x-54134=20640 \\ x=20640+54134 \\ x=74774 \end{gathered}[/tex]
The salary is $74,774.
2)
For z = -2, we have:
[tex]\begin{gathered} -2=\frac{x-54134}{10320} \\ x-54134=-20640 \\ x=-20640+54134 \\ x=33494 \end{gathered}[/tex]
The salary is $33,494.
3)
For z = 0, we have:
[tex]\begin{gathered} 0=\frac{x-54134}{10320} \\ x-54134=0 \\ x=54134 \end{gathered}[/tex]
The salary is $54,134.
4)
For z = 2.3, we have:
[tex]\begin{gathered} 2.3=\frac{x-54134}{10320} \\ x-54134=23736 \\ x=23736+54134 \\ x=77870 \end{gathered}[/tex]
The salary is $77,870.
5)
For z = -2.5, we have:
[tex]\begin{gathered} -2.5=\frac{x-54134}{10320} \\ x-54134=-25800 \\ x=-25800+54134 \\ x=28334 \end{gathered}[/tex]
The salary is $28,334.
