Intro to Business Statistics

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Normal distribution

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Intro to Business Statistics

Definition

A normal distribution is a continuous probability distribution that is symmetrical and bell-shaped, where most of the observations cluster around the central peak. It is characterized by its mean ($\mu$) and standard deviation ($\sigma$).

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5 Must Know Facts For Your Next Test

  1. The properties of a normal distribution include symmetry around the mean, a total area under the curve equal to 1, and asymptotic tails.
  2. In small sample cases when the population standard deviation is unknown, the t-distribution is often used instead of the normal distribution.
  3. The empirical rule states that approximately 68% of data falls within one standard deviation from the mean, about 95% within two standard deviations, and about 99.7% within three.
  4. Normal distributions are used to construct confidence intervals for estimating population parameters.
  5. When constructing confidence intervals with small samples (n < 30), itโ€™s important to verify that the sample data approximates a normal distribution.

Review Questions

  • What are the key properties of a normal distribution?
  • How does the t-distribution relate to the normal distribution in small sample cases?
  • What percentage of data falls within two standard deviations from the mean in a normal distribution?

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