Question

Is X~N($0,1$) a standardized normal distribution? Why or why not?

Short answer

It is clear that X follows standard deviation distribution because its mean is zero and the standard deviation is $1$.

Hence, X$~$N($0,1$) is a standard normal distribution.

Step-by-step solution

Given Information

Given the value that, X$~$N($0,1$)

Explanation

If a normal distribution is standardized then normal distribution will evolve standard normal distribution and then it can be defined as below:

Z$~$N($0,1$)

Where,

$\mu =0$

$\sigma =1$

It is given that X follows normal distribution such that,

X$~$N($0,1$)

So, it is clear that X follows standard deviation distribution because its mean is zero and the standard deviation is $1$.

Hence, X$~$N($0,1$) is standard normal distribution.