• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

Suggested languages for you:

Americas

Europe

Q.10

Expert-verified
Found in: Page 385

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

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

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.

See the step by step solution

## Step 1: Given Information

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

## Step 2: 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.