# Calculating probability in normal distribution
**URL:** https://discourse.julialang.org/t/calculating-probability-in-normal-distribution/40897
**Category:** Statistics
**Created:** [June 6, 2020, 10:47pm UTC](https://discourse.julialang.org/t/calculating-probability-in-normal-distribution/40897 "2020-06-06T22:47:07Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@Chris\_Anderson](https://discourse.julialang.org/u/Chris_Anderson)
#### Post date: [June 6, 2020, 10:47pm UTC](https://discourse.julialang.org/t/calculating-probability-in-normal-distribution/40897/1 "2020-06-06T22:47:07Z")
I want to calculate the probability of any particular value in a normal distribution. I suppose this is equivalent to calculating the percentile of a data point. Ideally some sort of function where I input a value and a mean and std and it outputs the percentage. Like looking at a z-score table…
Thank you.
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### Author:  [@Ian\_Slagle](https://discourse.julialang.org/u/Ian_Slagle)
#### Post date: [June 6, 2020, 11:00pm UTC](https://discourse.julialang.org/t/calculating-probability-in-normal-distribution/40897/2 "2020-06-06T23:00:51Z")
Something like this?
```julia
using Distributions
dist = Normal(3, 1)
cdf(dist, 1)
```
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### Author:  [@Chris\_Anderson](https://discourse.julialang.org/u/Chris_Anderson)
#### Post date: [June 6, 2020, 11:14pm UTC](https://discourse.julialang.org/t/calculating-probability-in-normal-distribution/40897/3 "2020-06-06T23:14:00Z")
That is exactly it. Thank you very much.
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### Author:  [@JesperMartinsson](https://discourse.julialang.org/u/JesperMartinsson)
#### Post date: [June 7, 2020, 10:12am UTC](https://discourse.julialang.org/t/calculating-probability-in-normal-distribution/40897/4 "2020-06-07T10:12:32Z")
Note that this is the probability of obtaining a value less than or equal to 1. The probability of obtaining a particular value is 0. 😉
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### Author:  [@Ian\_Slagle](https://discourse.julialang.org/u/Ian_Slagle)
#### Post date: [June 7, 2020, 3:04pm UTC](https://discourse.julialang.org/t/calculating-probability-in-normal-distribution/40897/5 "2020-06-07T15:04:18Z")
Right. And if you wanted the relative likelihood, you could use `pdf(dist, 1)`
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### Author:  [@Chris\_Anderson](https://discourse.julialang.org/u/Chris_Anderson)
#### Post date: [June 7, 2020, 4:18pm UTC](https://discourse.julialang.org/t/calculating-probability-in-normal-distribution/40897/6 "2020-06-07T16:18:39Z")
I know enough math/stats to know that, but thank you. Just implementing it via Julia, I was lost. Thanks again.
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### Author:  [@JesperMartinsson](https://discourse.julialang.org/u/JesperMartinsson)
#### Post date: [June 10, 2020, 10:10am UTC](https://discourse.julialang.org/t/calculating-probability-in-normal-distribution/40897/7 "2020-06-10T10:10:58Z")
I’m not sure that the term relative likelihood is the best for `pdf(dist,1)` since it returns the probability density for the value x=1 and not necessarily the likelihood. I guess for it to be called a likelihood the data should be fixed and the pdf is evaluated as a function of the parameter(s) in the distribution, i.e. over \mu or \sigma in the case we use a Normal distribution. For example, the likelihood given a known \sigma=1 and observed data x=1 would be something like `likelihood(mu) = pdf(Normal(mu,1),1) ` or `likelihood(sigma) = pdf(Normal(2,sigma),1) ` for known \mu=2 and x=1, or treating both parameters unknown.