Normal distribution or Gaussian distribution or Gauss distribution or Laplace–Gauss distribution, in probability theory, is a type of continuous probability distribution for a real-valued random variable. This post constitutes Lesson 5 of the Basic Statistics Mini-Course.
You may be also interested in Normal approximation to the binomial distribution.
Key concepts covered in this post: the normal curve (the normal probability curve), area probability graphs, using tables of areas under the normal curve, using N(0, 1) to investigate N(,2), standard deviation and the normal curve.
The normal curve
The normal probability curve is bell shaped and symmetric about the mean. The empirical rule (the three-sigma rule or 68-95-99.7 rule) states that for a normal distribution (Gaussian distribution) almost all observed data will fall within three standard deviations (σ) of the mean (µ). The rule predicts that 68% of observations fall within one standard deviation (µ ± σ), 95% within two standard deviations (µ ± 2σ), and 99.7% within three standard deviations (µ ± 3σ).
(Due to difficulties inserting some mathematical characters in WordPress, please finish reading this post in the embedded Google Doc below. You can jump to The standard normal curve.)
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