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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.

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Mathematical Equation for the Normal Distribution

The mathematical equation for the normal distribution:
y=e−(x−μ)22σ2σ2πy = \dfrac{e^{-\dfrac{(x - \mu)^2}{2\sigma^2}}}{\sigma\sqrt{2\pi}}
where:
  • e≈2.71828e \approx 2.71828
  • π≈3.14\pi \approx 3.14
  • μ=\mu = population mean
  • σ=\sigma = population standard deviation

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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
    one standard deviation of the mean is approximately 0.68 (68%).
    two standard deviations of the mean is approximately 0.95 (95%).
    three standard deviations of the mean is approximately 0.997 (99.7%).

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Areas Under the Normal Curve

Areas Under the Normal Curve