I saw in the Finnish matriculation examination solutions the sentence
If $X$ has the distribution $N(100,15)$, $Z=\frac{X-100}{15}$ has the distribution $N(0,1)$.
How one can memorize this? I mean I sometimes get confused whether it should be $Z=\frac{X-100}{15}$ or $Z=\frac{X-100}{\sqrt{15}}$. Or is it such that in this problem $15$ means the standard deviation and in for example the book Casella, Berger: "Statistical inference" it mean the variance?
Based on the definition of $Z$ it must be the case here that $15$ is the standard deviation. The distribution in question goes by two common names: the Normal and the Gaussian; from these arise the notations $N$ and $G$. In my experience, we write $N(\mu, \sigma^2)$ and $G(\mu, \sigma)$, where $\mu$ is the mean and $\sigma$ is the standard deviation, its square being the variance. This is the formula I've memorized: if $X$ is Normally distributed with mean $\mu$ and variance $\sigma^2$, then $\frac{X-\mu}{\sigma}$ is Normally distributed with mean $0$ and variance $1$.