# The Mth/prob Menu - Part 2; The Normal Distribution; The Student-t Distribution - HP 50g 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
2
the 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 UTPT, given the parameter
and the value of t, i.e.,
UTPT( ,t) = P(T>t) = 1-P(T<t). For example, UTPT(5,2.5) = 2.7245...E-2.
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