> ## Documentation Index
> Fetch the complete documentation index at: https://v1-learn.neoartd.my.id/llms.txt
> Use this file to discover all available pages before exploring further.

# The Standard Normal Distribution

The **standard normal distribution** is a
normal distribution with a mean of 0
and a standard deviation of 1.

> Distribusi normal standar adalah distribusi normal dengan rata-rata 0 dan simpangan baku 1.

All normally distributed variables can
be transformed into the standard
normally distributed variable by using
the formula for the standard score:

> Semua variabel yang didistribusikan secara normal dapat diubah menjadi variabel yang didistribusikan secara normal standar dengan menggunakan rumus untuk skor standar:

<Card>
  $z = \dfrac{value-mean}{standard deviation}$

  <br />

  or

  <br />

  $z = \dfrac{X-\mu}{\sigma}$
</Card>

### Area Under the Standard Normal Curve - Example

#### Question 1

<Card>
  Find the area under the standard
  normal curve between z = 0 and
  $z = 2.34 \rightarrow P(0 \leq z \leq 2.34)$.

  Use your table at the end of the text
  to find the area.

  <br />

  <img src="https://mintlify.s3.us-west-1.amazonaws.com/mmn/series/kuliah/2/statistika-dasar/7/images/screenshot-1715687421220.png" alt="Standard Normal Distribution" />
</Card>

#### Question 2

<Card>
  Find the area under the standard
  normal curve between z = 0 and
  $z = -1.75 \rightarrow P(-1.75 \leq z \leq 0)$.

  Use the symmetric property of the
  normal distribution and your table at
  the end of the text to find the area.

  <br />

  <img src="https://mintlify.s3.us-west-1.amazonaws.com/mmn/series/kuliah/2/statistika-dasar/7/images/screenshot-1715687490300.png" alt="Standard Normal Distribution" />
</Card>

#### Question 3

<Card>
  Find the area to the right of
  $z = 1.11 \rightarrow P(z > 1.11)$.

  Use your table at the end of the text
  to find the area.

  <br />

  <img src="https://mintlify.s3.us-west-1.amazonaws.com/mmn/series/kuliah/2/statistika-dasar/7/images/screenshot-1715687615873.png" alt="Standard Normal Distribution" />
</Card>

#### Question 4

<Card>
  Find the area to the left of
  $z = -1.93 \rightarrow P(z < -1.93>)$.

  Use the symmetric property of the
  normal distribution and your table at
  the end of the text to find the area.

  <br />

  <img src="https://mintlify.s3.us-west-1.amazonaws.com/mmn/series/kuliah/2/statistika-dasar/7/images/screenshot-1715687693167.png" alt="Standard Normal Distribution" />
</Card>

#### Question 5

<Card>
  Find the area between z = 2 and
  $z = 2.47 \rightarrow P(2 \leq z \leq 2.47)$.

  Use the symmetric property of the
  normal distribution and your table at
  the end of the text to find the area.

  <br />

  <img src="https://mintlify.s3.us-west-1.amazonaws.com/mmn/series/kuliah/2/statistika-dasar/7/images/screenshot-1715687767454.png" alt="Standard Normal Distribution" />
</Card>

#### Question 6

<Card>
  Find the area between z = 1.68 and
  $z = -1.37 \rightarrow P(-1.37 \leq z \leq 1.68)$.

  Use the symmetric property of the
  normal distribution and your table at
  the end of the text to find the area.

  <br />

  <img src="https://mintlify.s3.us-west-1.amazonaws.com/mmn/series/kuliah/2/statistika-dasar/7/images/screenshot-1715687852536.png" alt="Standard Normal Distribution" />
</Card>

#### Question 7

<Card>
  Find the area to the left of
  $z = 1.99 \rightarrow P(z < 1.99)$.

  Use your table at the end of the text
  to find the area.

  <br />

  <img src="https://mintlify.s3.us-west-1.amazonaws.com/mmn/series/kuliah/2/statistika-dasar/7/images/screenshot-1715687914289.png" alt="Standard Normal Distribution" />
</Card>

#### Question 8

<Card>
  Find the area to the right of
  $z = -1.16 \rightarrow P(z > -1.16)$.

  Use your table at the end of the text
  to find the area.

  <br />

  <img src="https://mintlify.s3.us-west-1.amazonaws.com/mmn/series/kuliah/2/statistika-dasar/7/images/screenshot-1715688001329.png" alt="Standard Normal Distribution" />
</Card>

## RECALL: The Standard Normal Distribution

<Card>
  $z = \dfrac{value-mean}{standard deviation}$

  <br />

  or

  <br />

  $z = \dfrac{X-\mu}{\sigma}$
</Card>