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 values of constants \( a \) and \( b \) given the transformations of the observations and their statistical properties.

### Step-by-Step Solution:

1. **Understanding the Transformation**:
We have \( y_i = ax_i + b \) for \( i = 1, 2, \ldots, n \). Here, \( a \) and \( b \) are constants that we need to determine.

2. **Given Information**:
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