If $y = - 8 x - 5$ and SD of $x$ is $3$ , then SD of $y$ is:

8

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24

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3

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None of these

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Solution

The correct option is B $24$
Given that std dev of x is $σ (x) = 3$
Given equation is $y = - 8 x - 5$

applying std dev on both sides we get

$σ (y) = σ (- 8 x - 5)$

$⟹ σ (y) = σ (- 8 x) + σ (- 5)$

$⟹ σ (y) = σ (- 8 x) + 0$ (since, $σ (c) = 0$ )

$⟹ σ (y) = 8 σ (x)$ (since, $σ (a X) = | a | σ (X)$ )

$⟹ σ (y) = 8 \times 3 = 24$

Therefore, standard deviation of $y$ is $24$ .

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