- Equality of Mean, Median, and Mode: In a normal distribution, the average (mean), middle value (median), and most frequent value (mode) are all the same.
- Positive Value: For any value of x, f(x) will have a positive value.
- Defined by Mean and Standard Deviation: A normal distribution is uniquely determined by two parameters, the average (mean) and the spread or variability (standard deviation). These parameters describe its uni-modal, bell-shaped, and symmetrical curve.
- Symmetry at the Center: A normal distribution curve is symmetrical. If you fold it in half at the center, both sides look the same. This means that the values on one side of the mean are like a mirror image of the other side.
- Total Area under the Curve: The entire area under the normal distribution curve adds up to 1. In simpler terms, if you add up all the probabilities of all possible values, it equals 100%.
- Half of Values on each side of the Center: Exactly half of the values are to the right of the center, and the other half is to the left of the center. This reflects the even distribution of data.
- One Peak: The normal distribution curve has only one hump or peak. It does not have multiple peaks. This is called a uni-modal distribution.
Normal Distribution in Business Statistics
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