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# Normal Distribution Definition and Quiz

Many of us were introduced to it when we first heard 'you will be graded on a curve' and now we can grasp how universally important it is.
1. Define - Define Normal Distribution for Finance.
2. Context - Use Normal Distribution in a sentence.
3. Quiz - Test yourself.
Updated: February 17, 2021
Understanding even the most basic statistical concepts can be a career differentiator. See an example of Excel's NORM.DIST function below.

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## Normal distribution definition

Beginner

Normal distribution is a probability distribution commonly used in Finance and other social sciences for statistical tests. There are several versions of the normal distribution, but the one called 'standard normal distribution' has a mean of 0 and standard deviation of 1 and is the default used to standardize data in spreadsheets and statistical analysis programming languages.

Synonyms: bell-shaped curve, Gaussian distribution, Gaussian function

For context, the normal distribution is one of several bell-shaped curves. One such distribution, the Student's T-distribution is often used in place of the normal distrbution when modeling stock returns because it reflects more observations in the tails, which is more aligned with historical stock returns.

Also, interestingly, in Excel, you can determine the probability of a sample value using an alternatively shaped normal distribution. You do this by supplying the `=NORM.DIST()` function these four items in succession.

1. Value - the observed sample value.
2. Mean - from the population.
3. Standard Deviation - from the population.
4. TRUE or FALSE - True for a cumulative distribution function and False for a probability mass function.

The cumulative distribution function shows the cumulative percentage of the distribution under, or to the left of, the observed value. This is akin to the probability of observations below the value.

So for example, imagine you had 60 monthly returns for each of 100 stocks and the average monthly return was 0.6%. Annualized, this would be about a 7.2% return. The standard deviation of all monthly observations was 5.0%, or an annualized standard deviation of 17.3%.

So to determine the probability of observations below the monthly return of 10.0% using this distribution, in Excel you could input `=NORM.DIST(0.1,0.006,0.05,TRUE)` for an answer of 0.9699. So, to interpret, 97% of observations would be predicted to fall below a return of 10.0%.

### In a Sentence

Bud:  Guy fails to realize that referring to the 'normal distribution' as 'Gaussian' is off-putting.
Rex:  Yeah, classic Quant. Most I know are at least two standard deviations from normal.

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### Quiz

The normal distribution is suitable for large and small sample sizes? | True or False

False. The t-distribution is better suited for small sample sizes.

The fourth parameter in Excel's =NORM.DIST() function to generate a cumulative distribution would require which input. | True or False

True. False returns a probabilty mass function which is better suited for discrete random variables instead of continuous.

Still unclear on the Normal Distribution for Finance? Check out our Quant 101 Series.

### Related Terms

Our trained humans found other terms in the category statistical distributions you may find helpful.

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