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

Answer:

$(a)\ \mu_y = 1125$

$(b)\ \sigma_y = 300$

Step-by-step 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:

$\sigma_y = \sqrt{Rate^2 * \sigma_2^2}$

This gives:

$\sigma_y = \sqrt{15^2 * 20^2}$

$\sigma_y = \sqrt{90000}$

$\sigma_y = 300$