Normal And Inverse-Normal Distributions - HP -32S Owner's Manual

Normal and Inverse-Normal Distributions
Normal distribution is frequently used to model the behavior of ran
dom variation about a mean. This model assumes that the sample
distribution is symmetric about the mean, M, with a standard devi
ation, S, and approximates the shape of the bell-shaped curve shown
below. Given a value x, this program calculates the probability that a
random selection from the sample data will have a higher value. This
is known as the upper tail area, Q(x). This program also provides the
inverse: given a value Q(x), the program calculates the corresponding
value x.
Q(x) - 0.5 -
V27
X
' e"«* - *> + •» + 2 ix.
This program uses the built-in integration feature of the HP-32S to
integrate the equation of the normal frequency curve. The inverse is
obtained using Newton's method to iteratively search for a value of x
which yields the given probability Q(x).
Program Listing:
Program Lines:
501 LBL S
502 0
503 STO M
504 INPUT M
Description:
This routines initializes the standard-
deviation program.
Stores default value for mean.
Prompts for and stores mean, M.
13: Statistics Programs 215