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?