Question

A real estate agent, working entirely on commission, makes a weekly average of $850 with da

standard deviation of $260 selling property in the city, and an average of $1340 with a standard
deviation of $390 selling property in the suburbs. Assuming independence, what are the mean and
standard deviation of her total weekly sales?

Answer 1

If the real estate agent's average weekly sales are $850 in the city and $1340 in the suburbs, then her total average weekly sales are $850 + $1340 = $2190.

The standard deviation of her weekly sales in the city is $260, and the standard deviation of her weekly sales in the suburbs is $390. If the sales in the city and the suburbs are independent, then the standard deviation of her total weekly sales is the square root of the sum of the squares of the standard deviations of her weekly sales in the city and the suburbs, which is the square root of $260^2 + $390^2 = $67600 + $152100 = $219100. This is equal to $468.

Therefore, the mean and standard deviation of the real estate agent's total weekly sales are $2190 and $468, respectively.