Question

question 1
1 pts
a standardized variable has mean

and standard deviation

. (enter numerical values for each blank.)

Explanation:

Step1: Recall standardization formula

The formula for standardizing a variable $X$ is $Z=\frac{X - \mu}{\sigma}$, where $\mu$ is the mean of $X$ and $\sigma$ is the standard - deviation of $X$. When $X$ is standardized to $Z$, the mean of $Z$ is calculated as $E(Z)=E(\frac{X - \mu}{\sigma})=\frac{E(X)-\mu}{\sigma}=\frac{\mu - \mu}{\sigma}=0$.

Step2: Recall standard - deviation of standardized variable

The standard - deviation of $Z$ is $SD(Z)=\sqrt{Var(Z)}$. Since $Var(Z)=Var(\frac{X - \mu}{\sigma})=\frac{1}{\sigma^{2}}Var(X)=\frac{\sigma^{2}}{\sigma^{2}} = 1$, then $SD(Z) = 1$.

Answer:

0
1