# The Mth/prob Menu - Part 2; The Normal Distribution; The Student-t Distribution - HP 49g+ User Manual

Graphing calculator.

## The MTH/PROB menu - part 2

In this section we discuss four continuous probability distributions that are
commonly used for problems related to statistical inference: the normal
2
distribution, the Student's t distribution, the Chi-square (
) distribution, and
the F-distribution. The functions provided by the calculator to evaluate
probabilities for these distributions are NDIST, UTPN, UTPT, UTPC, and UTPF.
These functions are contained in the MTH/PROBABILITY menu introduced
earlier in this chapter. To see these functions activate the MTH menu:
„ ´
and select the PROBABILITY option:

### The Normal distribution

Functions NDIST and UTPN relate to the Normal distribution with mean
,
2
and variance
.
To calculate the value of probability density function, or pdf, of the f(x) for the
2
normal distribution, use function NDIST( ,
,x). For example, check that for a
normal distribution, NDIST(1.0,0.5,2.0) = 0.20755374. This function is
useful to plot the Normal distribution pdf).
The calculator also provides function UTPN that calculates the upper-tail
normal distribution, i.e., UTPN( , , x) = P(X>x) = 1 - P(X<x), where P()
represents a probability. For example, check that for a normal distribution,
2
with
= 1.0,
= 0.5, UTPN(1.0,0.5,0.75) = 0.638163.

### The Student-t distribution

The Student-t, or simply, the t-, distribution has one parameter , known as the
degrees of freedom of the distribution. The calculator provides for values of
the upper-tail (cumulative) distribution function for the t-distribution, function
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