MathCastle
Statistics & DataSuperchallengeThe Normal Distribution

The Normal Distribution · Superchallenge problem

A machine fills bottles labelled 500500 ml. Fill volumes are normal with standard deviation 55 ml, and the operator sets the mean as low as possible subject to at most 2%2\% of bottles holding less than 500500 ml. With that setting, what fraction of bottles hold more than 520520 ml? Round to three decimal places.