Matlab calculates the integral of normal function, and the quantile corresponding to the integral

1. Find the integral value of normal distribution
$$f(x)={\int }_{-\infty }^x\frac{1}{\sqrt{2\pi }}exp[-\frac{(x-\mu {)}^2}{2{\sigma }^2}]dx$$
p = normcdf(x)
p = normcdf(x,mu)
p = normcdf(x,mu,sigma)

normcdf Function finding The mean for mu, The standard deviation is sigma Is a normal distribution , stay $[-\infty ,x]$ Integral on
among ,mu and sigma They are in the formula $\mu and\sigma$.

Example ：

%  The mean for 2, The variance of 1 Is a normal distribution , stay [-∞,2] Integral on 
>> normcdf(2,2,1)

ans =

    0.5000
    
%  The mean for 2, The variance of 1 Is a normal distribution , stay [1.1,2] Integral on 
 >> normcdf(2,2,1) - normcdf(1.1,2,1)

ans =

    0.3159

2. The integral value is known , Quantile $x$
x = norminv( p )
x = norminv( p,mu )
x = norminv( p,mu,sigma )

Example ：

%  The mean for 2, The variance of 1 Is a normal distribution , The integral value is 0.5 Quantile of time 
>> norminv(0.5,2,1)

ans =

     2
%  The standard normal distribution satisfies P{
    x0>x}=0.99
>> norminv(0.99)

ans =

    2.3263