::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the area under the normal density for a given one-sided or two-sided quantile value (Z-score), mean, and standard deviation. These computed probabilities are often displayed (in statistics handbooks) in the form of the so-called statistical tables about the normal distribution.
In addition, if a probability is specified, the software computes the quantiles (Z-scores) that correspond to the area under the normal density function.
You must enter (at least) a quantile value, or a probability value. You are allowed to enter both (the Z-score and the probability) at the same time.

---

Source code of R module

normal_prob_area_plot <- function(lb, ub, mean = 0, sd = 1, limits = c(mean - 4 * sd, mean + 4 * sd)) { x <- seq(limits[1], limits[2], length.out = 100) xmin <- max(lb, limits[1]) xmax <- min(ub, limits[2]) areax <- seq(xmin, xmax, length.out = 100) area <- data.frame(x = areax, ymin = 0, ymax = dnorm(areax, mean = mean, sd = sd)) plot(x, y = dnorm(x, mean = mean, sd = sd), type="l", lwd=2, col="blue", ylab = 'density') x = seq(lb,ub,length=100) y = dnorm(x) polygon(c(lb,x,ub), c(0,y,0), col = 'gray') } par5 <- as.numeric(par5) 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 <- round(pnorm(par1), par5) ru <- round(pnorm(par1,lower.tail=F), par5) rb <- round(pnorm(abs(par1)) - pnorm(-abs(par1)), par5) } print(r) print(ru) print(rb) if (par4 != "") { par4 <- as.numeric(par4) q1 <- round(qnorm(par4,par2,par3), par5) q1u <- round(qnorm(par4,par2,par3,lower.tail=F), par5) q2 <- round(qnorm((1-par4)/2,par2,par3,lower.tail=F), par5) } print(q1) print(q1u) print(q2) bitmap(file="test1.png") normal_prob_area_plot(lb = -4, ub = par1) dev.off() bitmap(file="test2.png") normal_prob_area_plot(lb = par1, ub = 4) dev.off() bitmap(file="test3.png") normal_prob_area_plot(lb = -abs(par1), ub = abs(par1)) dev.off() 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")

Cite this software as:

Wessa P., (2021), Normal CDF (v1.0.12), Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_cdfnorm.wasp/

The R code is based on :

Becker, R. A., Chambers, J. M. and Wilks, A. R., (1988), The New S Language, Wadsworth & Brooks/Cole.

Wichura, M. J. (1988) Algorithm AS 241: The Percentage Points of the Normal Distribution, Applied Statistics, vol. 37, 477-484.

To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

© All rights reserved. Academic license for non-commercial use only.
The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission.

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Software Version : 1.2.1
Algorithms & Software : Patrick Wessa, PhD
Server : wessa.net

About | Comments, Feedback & Errors | Privacy Policy | Statistics Resources | Wessa.net Home