Question

The Coff-E-Cup beverage company has opened two franchises in town. They put one location in the center of town and one at the west end of town. Let X be the number of customers that enter the center of town location in an hour, and Y be the number of customers that enter the location at the west end of town in an hour. Assuming that μX = 65 with σX = 4.3 and μY = 45 with σY = 3.2 , what is the mean of Z, the total number of customers that enter these locations in an hour?

Answer 1

The mean of Z, the total number of customers that enter these locations in an hour is 110.

Explanation:

Consider the provided information.

Let X be the number of customers that enter the center of town location in an hour,

Let Y be the number of customers that enter the location at the west end of town in an hour.

Assuming that
`\mu_X = 65\ with\ \sigma_X = 4.3\ and\ \mu_Y = 45\ with\ \sigma_Y = 3.2`

X and Y are independent random variables.

The expected value of the sum of random variables is equal to the sum of their individual expected values.

`E(X+Y)=E(X)+E(Y)\\=65+45=110`

Hence, the mean of Z, the total number of customers that enter these locations in an hour is 110.