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If the standard deviation of 2x(i) + 3 i...

If the standard deviation of `2x_(i) + 3` is 8 , then the variance of `(3x_(i))/(2)`.
(a) 24 (b) 36 (c) 6 (d) 18

Text Solution

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SD`(2x_(i)) + 3 = 8`
SD of `2x_(i) = 8 (because` SD does not alter when term is decreased by fixed constant.)
SD of `x_(i) = 4`
Variance of `x_(i) = SD^(2) = 16`
Variance of `(3x_(i))/(2) = ((9)/(4)) xx ` Variance of `x_(i) (because` Var (ax + b) = `a^(2) `Var(x))
`= ((9)/(4)) (16) = 36`
`therefore` Hence , option (b) is correct answer .
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