Maintenance script: Initial automated import

2016-02-24T18:21:02Z

Initial automated import

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{{Template:TI-BASIC:Command
|picture=INVNORM.GIF
|summary=Calculates the inverse of the cumulative normal distribution function.
|syntax=invNorm(''probability''[,''μ'', ''σ''])
|location=Press:
# 2ND DISTR to access the distribution menu
# 3 to select invNorm(, or use arrows.
|compatibility=TI-83/84/+/SE
|size=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 -1<span style="font-size: 75%">E</span>99 instead of negative infinity, and 1 will give 1<span style="font-size: 75%">E</span>99 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/+/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 [[TI-BASIC:Invt|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 [[TI-BASIC:Normalpdf|Normalpdf(]] and [[TI-BASIC:Normalcdf|Normalcdf(]] commands, the invNorm( command does not have a closed-form formula. It can however be expressed in terms of the [wikipedia:Error_function inverse error function]:
{{Template:TI-BASIC:Math
|eqn= \operatorname{invNorm}(p) = \sqrt{2}\,\operatorname{erf}^{-1}(2p-1)
}}

For the arbitrary normal distribution with mean μ and standard deviation σ:
{{Template:TI-BASIC:Math
|eqn= \operatorname{invNorm}(p,\mu,\sigma)=\mu+\sigma\operatorname{invNorm}(p)
}}

= Related Commands =

* [[TI-BASIC:Normalpdf|Normalpdf(]]
* [[TI-BASIC:Normalcdf|Normalcdf(]]
* [[TI-BASIC:Shadenorm|ShadeNorm(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Invnorm - Revision history

Maintenance script: Initial automated import