# What is the mean and std dev of the minimum of 6 random variables having a normal distribution?

###### Asked by peaceharris on January 16, 2014

Let’s say the average height of people is 150cm, with a std dev of 20cm, and their heights are normally distributed. Now if I group these people randomly in groups of 6 people, and I just take the height of the shortest person in each group. What is the mean and std dev of these shortest people?

## Answers

## The One Who Knows (Swamy)

## August 13, 2007 at 1:33 am

Without doing any maths, I would guess that the mean would be 147 cm and the standard deviation would remain same. But I could be wrong since I left statistics long ago.