Question

A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?

Short answer

The mean and standard deviation of Y is μY = $75, σY = $22.50

Step-by-step solution

Given information

$\mu$x = 50

$\sigma$x = 15

Explanation

Y = 1.50X

$\mu$aX+b = a$\mu$X+b

$\sigma$aX+b = $\left|a\right|$$\sigma$X

$\mu$Y =$\mu$1.5X = 1.5$\mu$