Question

A certain store sells only T-shirts. Let the random variable X represent the number of T-shirts bought from the store on any day, with a mean of 75 and a standard deviation of 20. Let the random variable Y be the total revenue from this store on a randomly selected day. If the store charges $15 per T-shirt, what are the mean and standard deviation of Y

Answer 1

`(a)\ \mu_y = 1125`

`(b)\ \sigma_y = 300`

Explanation:

Given

`\mu_x = 75` -- Mean of T-shirts

`\sigma_x = 20` -- Standard deviation of T-shirts

`Rate = \$ 15`

Solving (a): The mean of the revenue
`(\mu_y)`

To solve this, we use:

`\mu_y = Rate * \mu_x\\`

This gives:

`\mu_y = 15 * 75`

`\mu_y = 1125`

Solving (b): The standard deviation of the revenue
`(\sigma_y)`

To solve this, we use:

`\sigma_y = √(Rate^2 * \sigma_2^2)`

This gives:

`\sigma_y = √(15^2 * 20^2)`

`\sigma_y = √(90000)`

`\sigma_y = 300`