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 2…

Question

asked Apr 14, 2022 32.9k views

1 Answer

KingAm · Answer 1 · 2022-04-19T05:35:16+0000

Answer:

$(a)\ \mu_y = 1125$

$(b)\ \sigma_y = 300$

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:

$\sigma_y = √(15^2 * 20^2)$

$\sigma_y = √(90000)$

$\sigma_y = 300$