Question

A company employs 48 people in various departments. The average annual salary of each employee is $25,000 with a maximum variance of $3,000. What is the range of the total salary that the company pays to its employees annually?

Answer 1

Given:
n = 48, the sample size
m = $25,000, th sample mean
σ = $3000, the maximum variance

The standard deviation is
s = √σ = √(3000) = 54.772

As a rule of thumb, the range is 4 times the standard deviation. Therefore the range is
R = 4*54.772 = 219.09
Half the range is
R/2 = 219.09/2 = 109.45

The required  range is
(25000-109.45, 25000+109.45) = (24890.46, 25109.54)

Answer: ($24,890.46, $25,109.54)