Random variables can either be discrete or continuous. Continuous random variables can assume all values between any two given values of the variables. Many continuous random variables have distributions that are bell-shaped and are called approximately normally distributed variables.
The normal distribution, sometimes referred to as the Z distribution or Gaussian distribution, is considered the most important continuous probability distributions in statistics. This was named after a German mathematician who extensively studied the normal distribution. The graph of a normal distribution is called the normal curve. Variables that are normally distributed will have a mean and a standard deviation that may take on any value, but they share the following properties of the normal curve:
Figure 1. Normal Distribution Curve
1. The three measures of central tendency are located at the center of the normal curve.
2. The normal distribution curve is bell-shaped.
3. The normal distribution is unimodal.
4. The curve is symmetrical about the center.
5. The curve is continuous.
6. The curve is asymptotic with respect to the horizontal.
7. The total area above the horizontal axis under the normal distribution curve is equal to 1 or 100%.
8. The points of inflection of the curve occur at points plus or minus one standard deviation unit above or below the mean.
9. Roughly 68% of the area of the curve falls within the limits plus or minus one standard deviation unit from the mean.
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