Calculates the inverse of the cumulative normal distribution function.

invNorm(*probability*[,*μ*, *σ*])

Press:

- 2ND DISTR to access the distribution menu
- 3 to select invNorm(, or use arrows.

TI-83/84/+/SE

2 bytes

`invNorm(` is the inverse of the cumulative normal distribution function: given a probability, it will give you a z-score with that tail probability. The probability argument of `invNorm(` is between 0 and 1; 0 will give `-1E99` instead of negative infinity, and 1 will give `1E99` instead of positive infinity

There are two ways to use `invNorm(`. With three arguments, the inverse of the cumulative normal distribution for a probability with specified mean and standard deviation is calculated. With one argument, the standard normal distribution is assumed (zero mean and unit standard deviation). For example:

```
for the standard normal distribution
:invNorm(.975
for the normal distribution with mean 10 and std. dev. 2.5
:invNorm(.975,10,2.5
```

# Advanced

This is the only inverse of a probability distribution function available (at least on the TI-83/84/+/SE calculators), so it makes sense to use it as an approximation for other distributions. Since the normal distribution is a good approximation for a binomial distribution with many trials, we can use `invNorm(` as an approximation for the nonexistent "invBinom(". The following code gives the number of trials out of `N` that will succeed with probability `X` if the probability of any trial succeeding is `P` (rounded to the nearest whole number):

`:int(.5+invNorm(X,NP,√(NP(1-P`

You can also use `invNorm()` to approximate the inverse of a t-distribution. Since a normal distribution is a t-distribution with infinite degrees of freedom, this will be an overestimate for probabilities below 1/2, and an underestimate for probabilities above 1/2.

# Formulas

Unlike the `normalpdf(` and `normalcdf(` commands, the `invNorm(` command does not have a closed-form formula. It can however be expressed in terms of the inverse error function:

For the arbitrary normal distribution with mean μ and standard deviation σ:

(2)# Related Commands

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