Q.For a normal variable $X$ with mean $\mu$ and standard deviation $\sigma$, which of the following is standard normal variable $Z$ for it?

The standard normal variate is $Z=\dfrac{x-\mu}{\sigma}$.

To standardise a normal variable $X$ with mean $\mu$ and standard deviation $\sigma$, we measure how many standard deviations $x$ is from the mean: …

The standard normal variable has mean $0$ and variance $1$ — option (a).

GSEB Class-12 Statistics, Normal Distribution:

The standard normal variate is defined as:

$Z = \frac{X - \mu}{\sigma}$

…

True — the standard score $z = \dfrac{x-\mu}{\sigma}$ is dimensionless, so it does not depend on the unit of measurement.

GSEB Class-12 Statistics, Normal Distribution / Standardization:

The standard score is defined as:

$z = \frac{x - \mu}{\sigma}$

…

The standard normal variate $Z=\dfrac{X-\mu}{\sigma}$ has mean $0$ and variance $1$.

Reasoning. Standardising $X\sim N(\mu,\sigma^2)$ via $Z=\dfrac{X-\mu}{\sigma}$ shifts the mean to $0$ and scales th …