What is distribution of normal plus minus a constant? If $Y\sim N(\mu, \sigma^2)$, 

then $Y+\mu_0=N(\mu+\mu_0,\sigma^2)$ 

and $nY\sim N(n\mu, (n\sigma)^2)$. 

What about $-Y+\mu_0$? 

Will it give $N(\mu+\mu_0,(-\sigma)^2)$?
If $Y∼N(\mu,\sigma^2)$ then $-Y∼N(-\mu,\sigma^2)$. Thus $−Y+\mu_0~N(-\mu,\sigma^2)$
If $Y∼N(\mu,\sigma^2)$ then $-Y∼N(-\mu,\sigma^2)$. Thus $−Y+\mu_0~N(-\mu,\sigma^2)$