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What are the properties of normal distribution？

幫考網校2020-10-13 16:12:11
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The properties of normal distribution are:

1. Symmetry: The normal distribution is a symmetric distribution, which means that the left and right halves of the distribution are mirror images of each other.

2. Bell-shaped curve: The normal distribution has a bell-shaped curve, which means that the majority of the data falls in the middle of the distribution and the extreme values are less likely to occur.

3. Mean, median, and mode are equal: The mean, median, and mode are all equal in a normal distribution.

4. Standard deviation: The standard deviation determines the spread of the distribution. In a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% of the data falls within two standard deviations of the mean, and about 99.7% of the data falls within three standard deviations of the mean.

5. Empirical rule: The empirical rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.

6. Z-score: The z-score is a measure of how many standard deviations a data point is from the mean. In a normal distribution, the z-score can be used to determine the probability of a data point occurring.
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