Let `x_1, x_2, ,x_n` be `x_n` observations. Let `y_i=a x_i+b` for `i=1,2,...,n` where `a` and `b `are constants. If the mean of `x_i` is `48` and their standard deviation is `12`, the mean of `y_i` is `55` and standard deviation of `y_i` is `15`, the values of `a` and `b` are

Options

A. (a) `a=1.25 ,b=-5`
B. (b) `a=-1.25 ,b=5`
C. (c) `a=2.5 ,b=-5`
D. (d) `a=2.5 ,b=5`

Answer

(a) `a=1.25 ,b=-5`

Explanation

Given, `y_i=ax_i+b`


For `i = 1, 2, 3, ..., n`, where `a` and `b` are constants.

`bar x_i =48` and `sigma_(x_i)=12`

`bar y_i =55` and `sigma_(y_i)=15`


`y_i=ax_i+b`

`implies frac{Sigmay_i}{n}=frac{Sigma(ax_i+b)}{n}`


`implies frac{Sigmay_i}{n}=(afrac{Sigma(x_i)}{n}+frac{Sigmab}{n})`


`implies bary_i=abarx_i+b`


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