Question

If Var(x) = 25, then S.D. {(2x + 5)/2 ) is
equal to:
A 7.5
B 50
25
D 5​

Answer 1

Given :- If Var(x) = 25, then S.D. {(2x + 5)/2 ) is

equal to:

A) 7.5

B) 50

C) 25

D) 5

Answer :-

→ Variance(x) = 25

so,

→ SD(x) = √(Variance(x)

→ SD(x) = √(25) = 5

then,

→ SD(2x + 5)/2 = (2*5 + 5)/2

→ SD(2x + 5)/2 = (10 + 5)/2

→ SD(2x + 5)/2 = 15/2

→ SD(2x + 5)/2 = 7.5 (A) (Ans.)

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If Var(x) = 25, then $\displaystyle \sf{S.D \bigg( \frac{2x + 5}{2} \bigg) = }$

A. 7.5

B. 50

C. 25

D. 5

FORMULA TO BE IMPLEMENTED

We are aware of the formula from Statistics that

$\sf{1. \: \: Var (aX + b ) = {a}^{2} \: Var (X ) }$

$\sf{2. \: \: S.D(X) = + \sqrt{Var (X )} }$

EVALUATION

Here it is given that Var(x) = 25

Now

$\displaystyle \sf{Var \bigg( \frac{2x + 5}{2} \bigg)}$

$\displaystyle \sf{ = Var \bigg(x + \frac{ 5}{2} \bigg)}$

$\displaystyle \sf{ = {1}^{2} . Var (x )}$

$\displaystyle \sf{ = Var (x )}$

$\displaystyle \sf{ = 25}$

Now

$\displaystyle \sf{S.D \bigg( \frac{2x + 5}{2} \bigg)}$

$\displaystyle \sf{ = + \sqrt{Var \bigg( \frac{2x + 5}{2} \bigg)}}$

$\displaystyle \sf{ = + \sqrt{25}}$

$\displaystyle \sf{ = 5}$

FINAL ANSWER

Hence the correct option is D. 5

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