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Normal distribution

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Intro to Statistics

Definition

A normal distribution is a continuous probability distribution that is symmetrical around its mean, with a characteristic bell-shaped curve. In a normal distribution, most of the data points are concentrated around the mean, and the probabilities for values further away from the mean taper off equally in both directions.

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5 Must Know Facts For Your Next Test

  1. The mean, median, and mode of a normal distribution are all equal.
  2. Approximately 68% of the data in a normal distribution falls within one standard deviation of the mean.
  3. The total area under the curve of a normal distribution is equal to 1.
  4. Normal distributions are defined by two parameters: mean ($\mu$) and standard deviation ($\sigma$).
  5. The Z-score represents the number of standard deviations a data point is from the mean.

Review Questions

  • What percentage of data falls within one standard deviation of the mean in a normal distribution?
  • How are the mean, median, and mode related in a normal distribution?
  • What do $\mu$ and $\sigma$ represent in a normal distribution?

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