Normal distribution with CAS

You can solve different problems with normal distribution with CAS with only one function.[br]If randon variable [math]X\sim N\left(\mu,\sigma\right)[/math], then the cumulative distribution function is defined by [math]F\left(x\right)=P\left(X\le x\right)[/math]. [br][br]In Geogebra this function is: [br][math]normal\left(\mu,\sigma,x\right)[/math] or Normal(Mean ,Standard deviation , Variable Value).[br]By default, this gives cumulative distribution. For density you need to add 4th variable = false.[br]For example, you can graph density distribution with command[br]Normal( 10, 2, x, false).[br][br]But back to cumulative distribution. [br][br]You can solve problem: [math]\mu=10[/math] [math]\sigma=2[/math], solve [math]P\left(X<13.2\right)[/math] with command[br]Normal( 10, 2,13.2 )[br][br]Or the problem, where mean is unknow, but probability [math]P\left(X<13.2\right)=0.65[/math] is given, write equation[br]Normal(x, 2,13.2 )=0.65[br]and solve it numerically. For this you could also you function [br]InverseNormal( Mean, Standard Deviation,Probability).[br][br]Same works, when standard deviation is unknown. [br]Normal(11, x,13.2 )=0.65[br]Which problem is solved by this command? Remember to solve it numerically.[br][br]Try these out with Geogebra.

Information: Normal distribution with CAS