If the S.D. of x is 4, what is the variance of (5 - 2x)?

Option a: 64. Solution: Given: SD(x) = 4, so text{Var}(x) = 16 Find: text{Var}(5 - 2x) Using the property: text{Var}(a + bx) = b^2 text{Var}(x) Here a = 5, b = -2: text{Var}(5 - 2x) = (-2)^2 text{Var}(x) = 4 x 16 = 64 So text{Var}(5-2x) = 64 (Option A). The given correctoption 'd' (None of these) is incorrect since Option A (64) is the correct answer. Hence, Option A is the correct answer.

If the S.D. of $x$ is $4$, what is the variance of $(5 - 2x)$?

The correct answer is Option a: $64$. **Given:** $SD(x) = 4$, so $\text{Var}(x) = 16$ **Find:** $\text{Var}(5 - 2x)$ **Using the property:** $\text{Var}(a + bx) = b^2 \cdot \text{Var}(x)$ Here $a = 5$, $b = -2$: $$\text{Var}(5 - 2x) = (-2)^2 \cdot \text{Var}(x) = 4 \times 16 = 64$$ So $\text{Var}(5-2x) = 64$ (Option A). The given `correct_option` 'd' (None of these) is incorrect since Option A (64) is the correct answer. Hence, **Option A** is the correct answer.

Central Tendency & DispersionMTP Dec 2023 Series IIQuestion 3203 of 473

All Questions

If the S.D. of $\displaystyle x$ is $\displaystyle 4$ , what is the variance of $\displaystyle (5 - 2x)$ ?

Options

\displaystyle 64

\displaystyle 36

\displaystyle 16

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $\displaystyle 64$

All Options:

A $\displaystyle 64$
B $\displaystyle 36$
C $\displaystyle 16$
DNone of these

Detailed Solution & Explanation

**Given:**

\displaystyle SD(x) = 4

, so

\displaystyle \text{Var}(x) = 16

**Find:**

\displaystyle \text{Var}(5 - 2x)

**Using the property:**

\displaystyle \text{Var}(a + bx) = b^2 \cdot \text{Var}(x)

Here

\displaystyle a = 5

\displaystyle b = -2

\text{Var}(5 - 2x) = (-2)^2 \cdot \text{Var}(x) = 4 \times 16 = 64

\displaystyle \text{Var}(5-2x) = 64

(Option A). The given `correct_option` 'd' (None of these) is incorrect since Option A (64) is the correct answer. Hence, **Option A** is the correct answer.

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If the S.D. of x\displaystyle xx is 4\displaystyle 44, what is the variance of (5−2x)\displaystyle (5 - 2x)(5−2x)?