Answer
$R=45~thousand~dollars$
The population variance:
$σ^2=160~(thousand~dollars)^2$
The population standard deviation:
$σ=12.65~thousand~dollars$
They remain the same.
Work Step by Step
Adding the bonuses (+2.5 thousands of dollars each):
32.5, 32.5, 47.5, 52.5, 52.5, 52.5, 57.5, 57.5, 62.5, 77.5
$R=largest~value-smallest~value=77.5-32.5=45$
The mean:
$μ=\frac{32.5+32.5+47.5+52.5+52.5+52.5+57.5+57.5+62.5+77.5}{10}=52.5$
The population variance:
$σ^2=\frac{Σ(x_i-μ)^2}{n}=\frac{(32.5-52.5)^2+(32.5-52.5)^2+(47.5-52.5)^2+(52.5-52.5)^2+(52.5-52.5)^2+(52.5-52.5)^2+(57.5-52.5)^2+(57.5-52.5)^2+(62.5-52.5)^2+(77.5-52.5)^2}{10}=160$
The population standard deviation:
$σ=\sqrt {160}=12.65$
