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's` is 48 and their standard deviation is 12, the mean of `y_i 's` is 55 and standard deviation of `y_i's` is 15, the values of a and b are (a) `a=1. 25 ,b=-5` (b) `a=-1. 25 ,b=5` (c) `a=2. 5 ,b=-5` (d) `a=2. 5 ,b=5`

Explanation

To solve the problem, we need to find the constants \( a \) and \( b \) given the relationships between the means and standard deviations of the two sets of observations \( x_i \) and \( y_i \).

### Step 1: Write down the given information
- Mean of \( x_i \) (denoted as \( \bar{x} \)) = 48
- Standard deviation of \( x_i \) (denoted as \( \sigma_x \)) = 12
- Mean of \( y_i \) (denoted as \( \bar{y} \)) = 55
- Standard deviation of \( y_i \) (denoted as \( \sigma_y \)) = 15

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