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?

Answer 1

The mean of Y is $75 and the standard deviation of Y is $22.50.

Step-by-step explanation:

The mean of the random variable Y, which represents the total revenue from the vending machine, can be calculated by multiplying the mean number of bottles bought (50) by the price per bottle ($1.50). So the mean of Y is 50 * $1.50 = $75.

The standard deviation of Y can be calculated by multiplying the standard deviation of the number of bottles bought (15) by the price per bottle ($1.50). So the standard deviation of Y is 15 * $1.50 = $22.50.

Answer 2

The mean and standard deviation of a random variable can be used to describe the distribution of its possible values. In this case, the mean of the random variable X represents the average number of bottles of soda that are bought from the vending machine on a given day, and the standard deviation represents the amount of variation in the number of bottles bought from one day to the next.

To find the mean and standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, you will need to use the mean and standard deviation of X and the price per bottle of soda.

The mean of Y can be calculated using the formula:

mean of Y = mean of X * price per bottle

Plugging in the given values, we get:

mean of Y = 50 * $1.50 = $75

So the mean of the random variable Y, which represents the total revenue from the vending machine on a given day, is $75.

The standard deviation of Y can be calculated using the formula:

standard deviation of Y = standard deviation of X * price per bottle

Plugging in the given values, we get:

standard deviation of Y = 15 * $1.50 = $22.50

So the standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, is $22.50.

Therefore, the mean and standard deviation of Y, the total revenue from the vending machine on a given day, are $75 and $22.50, respectively.