Answer to Question #181453 in Statistics and Probability for Alice

Question

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. How many children belong to the upper 15% of the group?

Answer 1

Let's assume normal distribution with $\mu =110\; cm, \sigma=6\;cm$. The full integral of this distribution is 1. If we take 500 children and we want to find a number of children in some range in height, we want to multiple 500 by the area under the f(x) in the given range. Here, we know that this area is already 15%.

So, the number of children is $500 \cdot 0.15=75$

Answer: 75.