In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. It has applications in exploratory statistical graphics and specialized regression modeling of binary response variables.The standard normal distribution is commonly denoted as N(0,1) and its cumulative distribution function as . As an example, consider the familiar fact that the standard normal distribution places 95% of probability between −1.96 and 1.96, and is symmetric around zero. It follows thatThe probit function gives the 'inverse' computation, generating a value of an N(0,1) random variable, associated with specified cumulative probability. Formally, the probit function is the inverse of , denoted . Continuing the example,In general,