Normal And Inverse-Normal Distributions - HP 33s User Manual

To start:
R
M
B
y ˆ
Y ( when X =37)
x ˆ
X ( when Y =101)
Normal and Inverse–Normal Distributions
Normal distribution is frequently used to model the behavior of random variation
about a mean. This model assumes that the sample distribution is symmetric about
the mean, M, with a standard deviation, 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
This program uses the built–in integration feature of the HP 33s 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) .
Logarithmic
t
L
0.9965
–139.0088
65.8446
98.7508
38.2857
1
( x ) 0 5 .
Exponential
t
0.9945
51.1312
0.0177
98.5870
38.3628
y
Q [x]
x
x
x
∫
(( x x )
e
2
x
Statistics Programs
Power
t
E P
0.9959
8.9730
0.6640
98.6845
38.3151
"U p per tail"
area
2
) 2
dx
16–11