# Plotting Normal Distribution using formulas

**URL:** <https://community.wolfram.com/t/plotting-normal-distribution-using-formulas/16217>\
**Category:** Questions\
**Tags:** wolfram-alpha, graphics-and-visualization, statistics-and-probability\
**Created:** [June 18, 2020, 9:25pm UTC](https://community.wolfram.com/t/plotting-normal-distribution-using-formulas/16217 "2020-06-18T21:25:22Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![mattiasthalen](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@mattiasthalen](https://community.wolfram.com/u/mattiasthalen)\
**Post date:** [June 18, 2020, 9:25pm UTC](https://community.wolfram.com/t/plotting-normal-distribution-using-formulas/16217/1 "2020-06-18T21:25:22Z")

</div>

I’m trying to plot a normal distribution by using calculated the mu & sigma.

I can return the values of mu & sigma perfectly by using this query:

```
{mu=(22.3-y)*x^2, sigma=(1.9-y)*x^2} where y=6.1*(1.8-x) x=1.80

```

And I can return the plot by querying with:

```
NormalDistribution[72.252, 6.156]

```

I can’t however get the same result by doing

```
NormalDistribution[mu, sigma] where mu=(22.3-y)*x^2 sigma=(1.9-y)*x^2 y=6.1*(1.8-x) x=1.80

```

Anyone know how to write this as one query?

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<div class="post-metadata">

**Author:** ![rohitnamjoshi](https://avatars.discourse-cdn.com/v4/letter/r/f1d935/32.png) [@rohitnamjoshi](https://community.wolfram.com/u/rohitnamjoshi)\
**Post date:** [June 19, 2020, 1:50am UTC](https://community.wolfram.com/t/plotting-normal-distribution-using-formulas/16217/2 "2020-06-19T01:50:38Z")

</div>

x = 1.80; y = 6.1\*(1.8 - x); sigma = (1.9 - y) x^2; mu = (22.3 - y) x^2;  
nd = NormalDistribution[mu, sigma];  
Plot[PDF[nd, x], {x, mu - 4_sigma, mu + 4_sigma}]

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<div class="post-metadata">

**Author:** ![mattiasthalen](https://avatars.discourse-cdn.com/v4/letter/m/46a35a/32.png) [@mattiasthalen](https://community.wolfram.com/u/mattiasthalen)\
**Post date:** [June 19, 2020, 6:04am UTC](https://community.wolfram.com/t/plotting-normal-distribution-using-formulas/16217/3 "2020-06-19T06:04:27Z")

</div>

Did not work on WolframAlpha.  
The iOS app couldn’t interpret the input and the web app just returned the definition of the distribution, not actually evaluating it for x = 1.8

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<div class="post-metadata">

**Author:** ![anon\_91240867](https://avatars.discourse-cdn.com/v4/letter/a/8baadc/32.png) [@anon\_91240867](https://community.wolfram.com/u/anon_91240867)\
**Post date:** [June 19, 2020, 11:22am UTC](https://community.wolfram.com/t/plotting-normal-distribution-using-formulas/16217/4 "2020-06-19T11:22:35Z")

</div>

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