Central Tendency & DispersionMTP Nov 19/ MTP Sep 24 IIQuestion 3160 of 473
All Questions

If the SD of x\displaystyle x is 3\displaystyle 3, what us the variance of (5−x)\displaystyle (5-x)?

Options

A36\displaystyle 36
B6\displaystyle 6
C1\displaystyle 1
D9\displaystyle 9
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Correct Answer

✅ Option d — 9\displaystyle 9

All Options:

  • A36\displaystyle 36
  • B6\displaystyle 6
  • C1\displaystyle 1
  • D9\displaystyle 9

Detailed Solution & Explanation

**Given:** SD of x\displaystyle x = 3, so Var(x)=32=9\displaystyle \text{Var}(x) = 3^2 = 9 **Find:** Var(5−x)\displaystyle \text{Var}(5 - x) **Using the property:** Var(a+bx)=b2⋅Var(x)\displaystyle \text{Var}(a + bx) = b^2 \cdot \text{Var}(x) Here a=5\displaystyle a = 5, b=−1\displaystyle b = -1: Var(5−x)=(−1)2⋅Var(x)=1×9=9\text{Var}(5 - x) = (-1)^2 \cdot \text{Var}(x) = 1 \times 9 = 9 The correct answer is **9 (Option D)**. The given `correct_option` 'b' (6) is incorrect. Hence, **Option D** is the correct answer.

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