HP F2226A - 48GII Graphic Calculator - Normal Distribution Cdf

Page 17-10
],
2
)(
exp[
2
1
)(
2
2
σ
µ
πσ
−
−=
x
xf
where µ is the mean, and σ
2
is the variance of the distribution. To calculate
the value of f(µ,σ
2
,x) for the normal distribution, use function NDIST with the
following arguments: the mean, µ, the variance, σ
2
, and, the value x , i.e.,
NDIST(µ,σ
2
,x). For example, check that for a normal distribution,
f(1.0,0.5,2.0) = 0.20755374.
Normal distribution cdf
The calculator has a function UTPN that calculates the upper-tail normal
distribution, i.e., UTPN(x) = P(X>x) = 1 - P(X<x). To obtain the value of the
upper-tail normal distribution UTPN we need to enter the following values: the
mean, µ; the variance, σ
2
; and, the value x, e.g., UTPN((µ,σ
2
,x)
For example, check that for a normal distribution, with µ = 1.0, σ
2
= 0.5,
UTPN(0.75) = 0.638163. Use UTPN(1.0,0.5,0.75) = 0.638163.
Different probability calculations for normal distributions [X is N(µ,σ
2
)] can be
defined using the function UTPN, as follows:
• P(X<a) = 1 - UTPN(µ, σ
2
,a)
• P(a<X<b) = P(X<b) - P(X<a) = 1 - UTPN(µ, σ
2
,b) - (1 - UTPN(µ, σ
2
,a))
= UTPN(µ, σ
2
,a) - UTPN(µ, σ
2
,b)
• P(X>c) = UTPN(µ, σ
2
,c)
Examples: Using µ = 1.5, and σ
2
= 0.5, find:
P(X<1.0) = 1 - P(X>1.0) = 1 - UTPN(1.5, 0.5, 1.0) = 0.239750.
P(X>2.0) = UTPN(1.5, 0.5, 2.0) = 0.239750.
P(1.0<X<2.0) = F(1.0) - F(2.0) = UTPN(1.5,0.5,1.0) - UTPN(1.5,0.5,2.0)
= 0.7602499 - 0.2397500 = 0.524998.