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InvNorm Calculator

InvNorm Calculator




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An online invnorm calculator helps you to compute the inverse normal probability distribution and confidence interval for the given values. It also displays a graph for confidence level, left, right and two tails on the basis of probability, mean, standard deviation. Continue reading to how to use an inverse normal distribution in different fields of statistic.

What is Inverse Normal Distribution?

In statistics, the inverse normal distribution is an inverse working method of finding the value of x from a known probability. This is an informal term and does not involve any specific probability distribution.

You can use the given mean distribution and standard deviation to calculate the inverse cumulative normal distribution for a given x value. This function calculates the probability to the left of a certain value in the normal distribution.

For example, suppose we have a normally distributed random variable named x. For the x value, if we want to get the bottom 5% of the distribution, we can use the INVNORM function. As a financial analyst, this function is very useful when analyzing the stock market. We can use INVNORM to understand how the portfolio is affected by additions or exits.

Typically, TI-83 or TI-84 calculator used to find inverse normal distribution that is time-consuming task. Alternatively, you can use our free inverse normal calculator to determine the invnorm online.

Inverse Normal Formula:

The Invnorm formula uses the following parameters:

  • Probability (required parameter): Probability corresponding to a normal distribution. This is the value of the inverse function, which we want to evaluate the inverse normal function.
  • Mean (required parameter): Arithmetic mean of the distribution.
  • Standard deviation (required parameter): Standard deviation of distribution.

The inverse distribution is the continuous probability function defined by a formula, which used by invnorm calculator for invnorm function online:

$$ f(x, μ, σ) = 1 / ( \sqrt{2 π} σ ) e^{-(x – μ)}^2 / 2 σ^2 $$

μ = mean
σ = variance
x = independent variable

Inverse Normal Probability on a TI-83 or TI-84 Calculator:

The term “inverse normal distribution” on the TI-83 or TI-84 calculator, which uses the following function to find the critical x value corresponding to a given probability:

invNorm (probability, μ, σ)


Probability: significance level
μ: population mean
σ: population standard deviation

You can access this function on the TI-84 calculator by pressing 2nd and vars buttons. To make it convenient for you, our free norminv calculator can provide inverse normal probability distribution precisely with the value of probability, mean, and standard deviation.

For example, you use this function to find the critical z-value corresponding to the probability value of 0.05:
The critical z-value of corresponding to the distribution value of 0.05 is 1.64485.

Inverse Normal in Excel:

To find the critical value related to a certain probability value in Excel, we can use the INVNORM () function that uses the following syntax:

INVNORM (p, mean, sd)

p: significance level
mean: population mean
sd: population standard deviation

Important Points for NORM.INV Function:

  • When the mean is zero and the standard deviation is 1, NORM.INV uses the standard normal distribution.
  • # VALUE! Error- When any given parameter is non-numeric.
  • #NUM! Error-Occurs: When the specified probability parameter is less than 0 or greater than 1.
  • The standard deviation parameter is less than or equal to 0.

How does Invnorm Calculator Works?

An online inverse normal distribution calculator helps you to find inverse probability distribution by following steps:


  • First, substitute the values for Probability, Mean, and Standard Deviation.
  • Hit the calculate button.


  • The inverse norm calculator displays the values for left, right, two tails and standard deviation with graph.


What is the Difference Between Inverse Gaussian Distribution and Inverse Normal Distribution?

Inverse Gaussian is a two-parameter family of continuous distributions. The “inverse” in “inverse Gaussian” is misleading because distribution is not an inverse. The inverse distribution refers to the technique of searching backwards for the value of x. In other words, you found the opposite.

How do I know if my data is normally distributed?

A histogram is a useful graphical representation of some data. When the histogram of a distribution overlaps with its normal curve, the distribution is called a normal distribution.


From the source of Wikipedia: Relation to original distribution, Reciprocal distribution, Inverse uniform distribution, Inverse t distribution, Reciprocal normal distribution, Inverse exponential distribution.

From the source of Lumen Learning: Calculations of Probabilities, Standard Area Probability, Inverse exponential distribution, Inverse Cauchy distribution, Reciprocal of binomial distribution.

From the source of Brown Math: Calculations for Individuals, Calculations for Sample Means, Reciprocal of triangular distribution, Inverse distributions.