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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_cdfnorm.wasp

Title produced by software

Normal CDF

Date of computation

Sun, 16 Dec 2012 04:23:40 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/16/t1355649842vy43f8rcw7nzyl3.htm/, Retrieved Sun, 26 Oct 2025 03:33:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200180, Retrieved Sun, 26 Oct 2025 03:33:18 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

317

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Stem-and-leaf Plot] [] [2012-12-16 08:26:06] [5bd5238c609be1efcd3f9af130e08c87]
- RMPD    [Normal CDF] [] [2012-12-16 09:23:40] [14762276d088da8d9efe369819cbb035] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200180&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200180&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200180&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Normal Density Function
mean	0
standard deviation	1
Area under Normal Density
q value	1.96
z value	1.96
P[X <= z]	0.97500210485178
P[X > z]	0.0249978951482204
P[-\|z\| <= X <= \|z\|]	0.950004209703559
P[-\|z\| <= X] + P[X > \|z\|]	0.049995790296441
Quantiles
q given P[X <= q] = 0.95	1.64485362695147
q given P[X > q] = 0.95	-1.64485362695147
\|q\| given P[-\|q\| <= X] + P[X > \|q\|] = 0.05	1.95996398454005

\begin{tabular}{lllllllll}
\hline
Normal Density Function \tabularnewline
mean & 0 \tabularnewline
standard deviation & 1 \tabularnewline
Area under Normal Density \tabularnewline
q value & 1.96 \tabularnewline
z value & 1.96 \tabularnewline
P[X <= z] & 0.97500210485178 \tabularnewline
P[X > z] & 0.0249978951482204 \tabularnewline
P[-|z| <= X <= |z|] & 0.950004209703559 \tabularnewline
P[-|z| <= X] + P[X > |z|] & 0.049995790296441 \tabularnewline
Quantiles \tabularnewline
q given P[X <= q] = 0.95 & 1.64485362695147 \tabularnewline
q given P[X > q] = 0.95 & -1.64485362695147 \tabularnewline
|q| given P[-|q| <= X] + P[X > |q|] = 0.05 & 1.95996398454005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200180&T=1

[TABLE]
[ROW][C]Normal Density Function[/C][/ROW]
[ROW][C]mean[/C][C]0[/C][/ROW]
[ROW][C]standard deviation[/C][C]1[/C][/ROW]
[C]Area under Normal Density[/C][/ROW]
[ROW][C]q value[/C][C]1.96[/C][/ROW]
[ROW][C]z value[/C][C]1.96[/C][/ROW]
[ROW][C]P[X <= z][/C][C]0.97500210485178[/C][/ROW]
[ROW][C]P[X > z][/C][C]0.0249978951482204[/C][/ROW]
[ROW][C]P[-|z| <= X <= |z|][/C][C]0.950004209703559[/C][/ROW]
[ROW][C]P[-|z| <= X] + P[X > |z|][/C][C]0.049995790296441[/C][/ROW]
[C]Quantiles[/C][/ROW]
[ROW][C]q given P[X <= q] = 0.95[/C][C]1.64485362695147[/C][/ROW]
[ROW][C]q given P[X > q] = 0.95[/C][C]-1.64485362695147[/C][/ROW]
[ROW][C]|q| given P[-|q| <= X] + P[X > |q|] = 0.05[/C][C]1.95996398454005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200180&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200180&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Normal Density Function
mean	0
standard deviation	1
Area under Normal Density
q value	1.96
z value	1.96
P[X <= z]	0.97500210485178
P[X > z]	0.0249978951482204
P[-\|z\| <= X <= \|z\|]	0.950004209703559
P[-\|z\| <= X] + P[X > \|z\|]	0.049995790296441
Quantiles
q given P[X <= q] = 0.95	1.64485362695147
q given P[X > q] = 0.95	-1.64485362695147
\|q\| given P[-\|q\| <= X] + P[X > \|q\|] = 0.05	1.95996398454005

Parameters (Session):

par1 = 1.96 ; par2 = 0 ; par3 = 1 ; par4 = 0.95 ;

Parameters (R input):

par1 = 1.96 ; par2 = 0 ; par3 = 1 ; par4 = 0.95 ;

R code (references can be found in the software module):

par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
if (par3 <= 0) par3 = 1
if (par1 != '') {
par1 <- as.numeric(par1)
oldpar1 <- par1
par1 <- (par1 - par2) / par3
r <- pnorm(par1)
ru <- pnorm(par1,lower.tail=F)
rb <- pnorm(abs(par1)) - pnorm(-abs(par1))
}
r
ru
rb
if (par4 != '') {
par4 <- as.numeric(par4)
q1 <- qnorm(par4,par2,par3)
q1u <- qnorm(par4,par2,par3,lower.tail=F)
q2 <- qnorm((1-par4)/2,par2,par3,lower.tail=F)
}
q1
q1u
q2
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Normal Density Function',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'mean',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'standard deviation',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
if (par1 != '') {
a<-table.element(a,'Area under Normal Density',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'q value',header=TRUE)
a<-table.element(a,oldpar1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'z value',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'P[X <= z]',header=TRUE)
a<-table.element(a,r)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'P[X > z]',header=TRUE)
a<-table.element(a,ru)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'P[-|z| <= X <= |z|]',header=TRUE)
a<-table.element(a,rb)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'P[-|z| <= X] + P[X > |z|]',header=TRUE)
a<-table.element(a,1-rb)
a<-table.row.end(a)
}
if (par4 != '') {
a<-table.element(a,'Quantiles',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
dum <- paste('q given P[X <= q] = ',par4,sep='')
a<-table.element(a,dum,header=TRUE)
a<-table.element(a,q1)
a<-table.row.end(a)
a<-table.row.start(a)
dum <- paste('q given P[X > q] = ',par4,sep='')
a<-table.element(a,dum,header=TRUE)
a<-table.element(a,q1u)
a<-table.row.end(a)
a<-table.row.start(a)
dum <- paste('|q| given P[-|q| <= X] + P[X > |q|] = ',1-par4,sep='')
a<-table.element(a,dum,header=TRUE)
a<-table.element(a,q2)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code