If you apply a linear transformation
[tex]aX+b[/tex]
to a random variable X, the mean and standard deviations change as follows:
[tex]\mathbb{E}(aX+b)=a\mathbb{E}(X)+b[/tex]
[tex]\sigma(aX+b)=a\sigma(X)[/tex]
So, the new mean is
[tex]3\cdot 5+4=15+4=19[/tex]
and the new standard deviation is
[tex]3\cdot 2=6[/tex]
