# normal distribution

## noun

: a probability density function that approximates the distribution of many random variables (such as the proportion of outcomes of a particular kind in a large number of independent repetitions of an experiment in which the probabilities remain constant from trial to trial) and that has the form {latex}f(x) = \frac{1}{\sqrt{2\pi\sigma^{2}}}e^{-\frac{(x - \mu)^{2}}{2\sigma^{2}}}{/latex} where μ is the mean and σ is the standard deviation compare normal curve

## Examples of normal distribution in a Sentence

Recent Examples on the Web Second, the initial velocities will have a normal distribution of speeds and will start off in random directions. Rhett Allain, WIRED, 21 Jan. 2024 Assuming a normal distribution that's a 1 in 20 million probability. Razib Khan, Discover Magazine, 21 Feb. 2010 Additionally, there's a normal distribution of the trait. Razib Khan, Discover Magazine, 20 July 2011 Problem Two: Unusual People In the normal distribution, the next algorithm is premised on the most likely next correlation, and the most likely next correlation after that. Nancy Doyle, Forbes, 7 May 2023 Going back to height, the plot to the left shows an idealized normal distribution of height for males. Razib Khan, Discover Magazine, 24 Dec. 2011 With a normal distribution, that would mean that most American men would be between 69.9 and 70.1 inches tall—essentially all the same size. Rhett Allain, WIRED, 23 Dec. 2022 In a normal distribution that's the ~2% tail at the ends. Razib Khan, Discover Magazine, 12 Jan. 2011 This implies that variation in phenotype is controlled by variation across many genes, and, that the variation itself exhibits gradual continuity (a continuity which can be modeled as a normal distribution of values). Razib Khan, Discover Magazine, 9 Jan. 2011

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'normal distribution.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## Word History

First Known Use

1897, in the meaning defined above

Time Traveler
The first known use of normal distribution was in 1897

## Dictionary Entries Near normal distribution

normal distribution

## Cite this Entry

“Normal distribution.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/normal%20distribution. Accessed 15 Apr. 2024.

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