consider the theoretical boxplot of a general normal distribution with a mean and standard deviation and find the probability of being an outlier according to the 1.5*IQR criterion:
first, find the z-score of the lower/upper quartile .I.e. the value of z that makes ±z* indicate the lower/upper quartile.
second, use this to find the Inner Quartile Range (expressed in terms of )
third, find the z-score of the maximal extent of the whisker.I.e. the value of z that makes ±z* indicate the endpoint of the lower/upper whisker
finally, find the probability of being an outlier