Answer-first summary for fast verification
Answer: 720
## Explanation Let X be the original living costs with: - Mean(X) = $3,000 - Variance(X) = $500 The new living costs Y after adding 20% tax is: ``` Y = 1.2X ``` Using the variance property: Var(aX) = a²Var(X) ``` Var(Y) = Var(1.2X) = (1.2)² × Var(X) = 1.44 × 500 = 720 ``` **Key Points:** 1. Variance is affected by scaling factor squared 2. Mean would also change: Mean(Y) = 1.2 × 3000 = $3,600 3. The original mean of $3,000 is not needed for variance calculation 4. Standard deviation would be: σ_Y = 1.2 × σ_X = 1.2 × √500 ≈ 1.2 × 22.36 = 26.83 Therefore, the new variance is **720**.
Author: Nikitesh Somanthe
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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
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