Answer to Question #330237 in Statistics and Probability for diana

Question

The weights of students in a certain school are normally distributed with a mean weight of 66 kg. 10% have a weight greater than 70kg. What percentage of students weighs between 62kg and 66kg?

Answer 1

The normal distribution is symmetric:

$P(W\le66)=P(W\ge66)=50\%\\ P(66-4=62\le W\le66)=\\ =P(66\le W\le70=66+4)=\\ =50\%-P(70\le W)=40\%$