| Command Summary | Command Syntax | Calculator Compatibility | Token Size |
|---|---|---|---|
| Evaluates the normal probability density function at a point. | normalpdf(x[,μ, σ]) | TI-83/84/+/SE | 2 bytes |
Menu Location
Press:
1. 2ND DISTR to access the distribution menu
2. ENTER to select normalpdf(.
The normalpdf( Command
normalpdf( is the normal (Gaussian) probability density function.
Since the normal distribution is continuous, the value of normalpdf( doesn't represent an actual probability - in fact, one of the only uses for this command is to draw a graph of the normal curve. You could also use it for various calculus purposes, such as finding inflection points.
The command can be used in two ways: normalpdf(x) will evaluate the standard normal p.d.f. (with mean at 0 and a standard deviation of 1) at x, and normalpdf(x,μ,σ) will work for an arbitrary normal curve, with mean μ and standard deviation σ.
Formulas
For the standard normal distribution, normalpdf(x) is defined as
$$ \operatorname{normalpdf}(x)=\frac1{\sqrt{2\pi\,}} \, e^{-\frac1{2}x^2} $$
For other normal distributions, normalpdf( is defined in terms of the standard distribution:
$$ \operatorname{normalpdf}(x,\mu,\sigma)=\frac{1}{\sigma} \, \operatorname{normalpdf} \left(\frac{x-\mu}{\sigma}\right) $$