> ## 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.

# Properties of the Normal Distribution

Many continuous variables have distributions that are bell-shaped and are called **approximately normally distributed variables.**

> Banyak variabel kontinu memiliki distribusi yang berbentuk lonceng dan disebut **variabel yang didistribusikan secara normal.**

The theoretical curve, called the **normal
distribution curve**, can be used to study
many variables that are not normally
distributed but are approximately normal.

> Kurva teoritis, yang disebut **kurva distribusi normal**, dapat digunakan untuk mempelajari banyak variabel yang tidak didistribusikan secara normal tetapi hampir normal.

## Mathematical Equation for the Normal Distribution

<Card>
  The mathematical equation for the normal distribution:

  <br />

  $y = \dfrac{e^{-\dfrac{(x - \mu)^2}{2\sigma^2}}}{\sigma\sqrt{2\pi}}$

  <br />

  where:

  * $e \approx 2.71828$
  * $\pi \approx 3.14$
  * $\mu =$ population mean
  * $\sigma =$ population standard deviation
</Card>

## Properties of the Theoretical Normal Distribution

* The shape and position of the normal
  distribution curve depend on two
  parameters, the mean and the standard
  deviation.

  > Bentuk dan posisi kurva distribusi normal tergantung pada dua parameter, yaitu rata-rata dan simpangan baku.

* Each normally distributed variable has
  its own normal distribution curve,
  which depends on the values of the
  variable's mean and standard deviation.

  > Setiap variabel yang didistribusikan secara normal memiliki kurva distribusi normal sendiri, yang tergantung pada nilai rata-rata dan simpangan baku variabel tersebut.

* The normal distribution curve is
  bell-shaped.

  > Kurva distribusi normal berbentuk lonceng.

* The mean, median, and mode are
  equal and located at the center of the
  distribution.

  > Rata-rata, median, dan modus sama dan terletak di tengah distribusi.

* The normal distribution curve is
  unimodal (single mode).

  > Kurva distribusi normal unimodal (satu modus).

* The curve is symmetrical about the
  mean.

  > Kurva simetris terhadap rata-rata.

* The curve is continuous.

  > Kurva kontinu.

* The curve never touches the x-axis.

  > Kurva tidak pernah menyentuh sumbu x.

* The total area under the normal
  distribution curve is equal to 1.

  > Luas total di bawah kurva distribusi normal sama dengan 1.

* The area under the normal curve that
  lies within

  > Luas di bawah kurva normal yang terletak di dalam

  <Check>one standard deviation of the mean is approximately 0.68 (68%).</Check>

  <Check>
    two standard deviations of the mean is approximately 0.95 (95%).
  </Check>

  <Check>
    three standard deviations of the mean is approximately 0.997 (99.7%).
  </Check>

## Areas Under the Normal Curve

<img src="https://mintlify.s3.us-west-1.amazonaws.com/mmn/series/kuliah/2/statistika-dasar/7/images/screenshot-1715686836917.png" alt="Areas Under the Normal Curve" />