Answer-first summary for fast verification
Answer: 720
## Explanation For this exercise, we need to find the variance of new living costs. Let X be the old living costs and Y the new living costs, then we have: ``` Y = 1.2X Var(Y) = Var(1.2X) = 1.44 Var(X) = 1.44(500) = 720 ``` **Key Concept:** When a random variable is multiplied by a constant, the variance is multiplied by the square of that constant. This is expressed as: `Var(aX) = a²Var(X)` Where: - `a = 1.2` (20% increase) - `Var(X) = 500` (original variance) - `Var(Y) = (1.2)² × 500 = 1.44 × 500 = 720` Note that the mean ($3,000) is not needed for calculating the variance, as variance measures spread around the mean, not the mean itself.
Author: Tanishq Prabhu
Ultimate access to all questions.
Living in a certain city is really expensive. The mean spent by a citizen monthly is $3,000 with a variance of $500. Nonetheless, the city mayor decided to put a tax in order to make people regulate their monthly expenses adding 20% to all daily living articles. Find the new variance of this city.
A
520
B
580
C
600
D
720
No comments yet.