# NORM.INV

The `NORM.INV` function returns the inverse of the cumulative normal distribution for a specified mean and standard deviation. It is commonly used in statistical analysis to find the value at which a specified percentage of observations occur below that value.

## Usage

Use the `NORM.INV` formula with the syntax shown below, it has 3 required parameters:

Parameters:
1. x (required):
The probability of the value occurring below the mean.
2. mean (required):
The arithmetic mean of the distribution.
3. standard_deviation (required):
The standard deviation of the distribution.

## Examples

Here are a few example use cases that explain how to use the `NORM.INV` formula in Google Sheets.

### Finding the z-score for a given probability

Suppose we want to find the z-score for which there is a 25% chance of getting a value lower than that. We can use `NORM.INV` with `x = 0.25`, `mean = 0` and `standard_deviation = 1` to find this value.

### Generating a random sample from a normal distribution

We can use the `RAND` function along with `NORM.INV` to generate a random sample from a normal distribution with a given mean and standard deviation. Setting `x = RAND()`, `mean` and `standard_deviation` as desired, we can generate a random number that follows a normal distribution.

### Calculating confidence intervals

Suppose we have a dataset with a normal distribution and we want to calculate a confidence interval for the mean. We can use `NORM.INV` along with other functions such as `AVERAGE`, `STDEV.S` and `COUNT` to calculate the confidence interval for a specified confidence level.

## Common Mistakes

`NORM.INV` not working? Here are some common mistakes people make when using the `NORM.INV` Google Sheets Formula:

### Incorrect arguments

One of the arguments provided is incorrect or in the wrong order. Double-check the syntax and ensure that the arguments are entered in the correct order.

### Invalid mean or standard deviation

The mean or standard deviation provided is invalid (e.g. negative). Ensure that the mean and standard deviation are valid values.

### Non-numeric input

The input provided for x, mean, or standard_deviation is not a number. Check that the input is numeric and formatted correctly.

The following functions are similar to `NORM.INV` or are often used with it in a formula:

• `NORM.S.INV`

The `NORM.S.INV` function is a statistical function in Google Sheets that returns the inverse of the standard normal cumulative distribution function for a specified value. In other words, it returns the z-score that corresponds to a given probability. This function is commonly used in hypothesis testing, confidence interval estimation, and other statistical analyses.

• `NORM.DIST`

The `NORM.DIST` formula is a statistical function that returns the normal distribution of a specified variable. It is used to determine the probability of a random variable falling within a specified range of values. This function is commonly used in finance and scientific research.

• `NORM.S.DIST`

The NORM.S.DIST function returns the standard normal cumulative distribution function. It calculates the probability that a random variable with a standard normal distribution is less than or equal to x. This function is commonly used in statistical analysis and hypothesis testing.

• `STDEV.P`

The `STDEV.P` function is a statistical function that calculates the standard deviation of a population based on a sample of numerical data. It is commonly used to measure the amount of variation or dispersion in a dataset. The formula assumes that the input values represent the entire population, rather than a sample. If the input values represent a sample, you should use the `STDEV.S` function instead.

• `AVERAGE`

The AVERAGE function calculates the average (arithmetic mean) of the values passed to it. It is commonly used to find the average of a range of cells containing numerical data.

You can learn more about the `NORM.INV` Google Sheets function on Google Support.