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 eitans total monthly salary? choose 1 answer:

Explanation:

Step1: Calculate the mean of the commission

The mean of sales is $\$8000$. The commission is $30\%$ of sales. So the mean of the commission is $0.3\times8000 = 2400$.

Step2: Calculate the mean of the total - salary

The base salary is $\$2000$. The mean of the total - salary is the sum of the mean of the commission and the base salary. So, $\text{Mean of total salary}=2400 + 2000=4400$.

Step3: Calculate the standard deviation of the total - salary

The standard deviation of sales is $\$1500$. The commission is $30\%$ of sales. Since the base salary is a constant and adding a constant to a random variable does not change its standard deviation, the standard deviation of the total - salary is the same as the standard deviation of the commission. The standard deviation of the commission is $0.3\times1500 = 450$.

Answer:

The mean of Eitan's total monthly salary is $\$4400$ and the standard deviation is $\$450$.