Answer : Samuel salary falls within the standard deviation and his salary is not abnormal
The mean annual salary at the company where samuel works is $37, 000
The standard deviation is given as $4, 000
Samule's annual salary is $32, 500
Using the Z- score formula
[tex]\begin{gathered} z\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ \text{Where x = sample score} \\ \mu\text{ = mean} \\ \sigma\text{ = standard deviation} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = \$32, 500} \\ \mu\text{ = \$37, 000} \\ \sigma=\text{ \$ 4000} \\ z\text{ = }\frac{32,\text{ 500 - 37000}}{4000} \\ z\text{ = }\frac{-4500}{4000} \\ z\text{ = -1.125} \end{gathered}[/tex]Since, the value of Z- score is -1. 125, then, the salary is 1 standard deviation below the mean.
Therefore, Samuel salary falls within the standard deviation and his salary is not abnormal
