3. A researcher has collected data on the heights of a sample of adults but has encoded the actual values using a linear transformation of the form \(a X + b\), where \(X\) represents the original height in centimetres.
Given the following information about the encoded data:
The mean of the encoded heights is 5.4 cm
The standard deviation of the encoded heights is 2.0 cm
The researcher knows that the transformation used was \(0.2 X - 30\)

1. Find the mean of the original heights in the sample.
2. Find the standard deviation of the original heights in the sample.
3. If an encoded height value is 6.8 , what was the original height in centimetres?
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