Question

You are working with the marketing team for a FMCG firm that produces shaving cream. The team believes that sales of some of the products are closely related to sales of other products. They want you to explore this in a little more depth for two products, SKU 123 and SKU 456. Unfortunately, all of the base sales data for these products has been destroyed. All that you have is the weekly summary data:

Data Mean Standard Deviation

SKU123 721 176

SKU456 1059 266

Now the marketing team wants to understand the potential weekly sales for these two products. Let the sales price for the two SKUs be 12.50, 7.75, respectively.

1) What is the expected weekly revenue?

2) What is the standard deviation of the weekly revenue?

3) Assuming the marketing team’s correlation of 0.79 is correct. What is the probability that weekly sales will be between 10,000 and 20,000 dollars?

Answer 1

We are given the following details:

DATA	SKU123	SKU456
Mean	721	1059
Standard Deviation	176	266
Sales Price	12.50	7.75

(1) Suppose X denotes the expected revenue from product SKU123 and Y denotes the expected revenue from product SKU456. Then the total revenue es:

Revenue = X + Y

where X = Mean number of units of SKU123 * Sales Price

and Y = Mean number of units of SKU456 * Sales Price

Thus Revenue = 9012.5 + 8207.25 = 17219.75

Thus the expected weekly revenue is 17219.5.

(2) The standard deviation of the revenue from  product SKU123 is:

and the standard deviation of the revenue from  product SKU456 is:

(3) Assuming that the correlation between the sales of the two products is 0.79 then the standard deviation of the total weekly revenue is:

Thus the probability that the weekly revenue will be between 10,000 and 20,000 dollars is given as:

Standardising the above probability we have:

Thus the required probability is 0.718.