Question

Eitan sells a mean of $8000 worth of merchandise with a standard deviation of $1500 each month.

Each month, Eitan earns a base salary of $2000 plus a commission of 30% of his sales. He calculates his total

salary according to this formula:

[total salary) = commission + base salary]

What will be the mean and standard deviation of the distribution of Eitan's total monthly salary?

Answer 1

t = $4400 +/- $450

mean = $4400

standard deviation = $450

Explanation:

Given;

Base salary b = $2000

Sales s = $8000 +/- $1500

Commission c = 30% sales = 0.3 × s

Total Salary t = base salary + commission = b + c

Commission c = 0.3×s = 0.3×($8000 +/-$1500)

c = $2400 +/- $450

Total salary t = b + c

Substituting the values;

t = $2000 + ($2400 +/- $450)

t = $4400 +/- $450

mean = $4400

standard deviation = $450