$\begin {array} {1 1} (A)\;\large\frac{a}{c} \sigma & \quad (B)\;|\large\frac{a}{c}| \sigma \\ (C)\;|\large\frac{c}{a}| \sigma & \quad (D)\;\large\frac{c}{a} \sigma \end {array}$

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Let $ Y = \large\frac{aX+b}{c}$

$ \Rightarrow \overline Y = \large\frac{a\overline X +b}{c}$

$ \Rightarrow Y-\overline Y = \large\frac{a}{c} ( X - \overline X)$

$ \large\frac{1}{N} $$ \Sigma ( Y - \overline Y )^2 = \large\frac{a^2}{c^2}$ $ \large\frac{1}{N}$$ \Sigma ( X - \overline X )^2$

$ \sigma_y^2=\large\frac{a^2}{c^2} \sigma^2$

$ \sigma_y= |\large\frac{a}{c} | \sigma$

Ans : (B)

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