Kyle D. S. Maclean

Business Analytics Teaching Resources for Management Science/Operations Research

Finding CDFs of normal distributions on Canvas Quizzes

Canvas quizzes have a wonderful feature called "Formula" answers, where a question can have randomized numbers for each student. When creating these types of questions, you must enter the final correct answer as a formula based on the random variables. The problem is that these formulas do not include many statistical functions.

The CDF of a normal distribution with mean M and standard deviation S can be approximated at point X with the following formula

1/(1+e^(-0.07056*(((X-M)/(S))^3)-1.5976*((X-M)/(S))))

This approximation was proposed by Bowling et al (2009).

Keep in mind that it is only a very good approximation, so I usually only check answers to the first or second decimal place.