Question

The mean annual salary at the company where Samuel works is $37,000, with standard deviation $4,000. Samuel's salary is $32,500. Based on the mean and standard deviation, is Samuel's salary abnormal compared to other salaries at this company? When choosing your answer, be careful to select the answer with the correct explanation. A. Samuel's salary falls within the standard deviation, so his salary is not abnormal compared to other salaries at this company. B. Samuel's salary falls outside the standard deviation, so his salary is abnormal compared to other salaries at this company. C. Samuel's salary falls within the standard deviation, so his salary is abnormal compared to other salaries at this company. D. Samuel's salary falls outside the standard deviation, so his salary is not abnormal compared to other salaries at this company?

Answer 1

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

`\begin{gathered} z\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ \text{Where x = sample score} \\ \mu\text{ = mean} \\ \sigma\text{ = standard deviation} \end{gathered}`
`\begin{gathered} x\text{ = \$32, 500} \\ \mu\text{ = \$37, 000} \\ \sigma=\text{ \$ 4000} \\ z\text{ = }\frac{32,\text{ 500 - 37000}}{4000} \\ z\text{ = }(-4500)/(4000) \\ z\text{ = -1.125} \end{gathered}`

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