Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

Looking for tall basketball players

A certain country with a large population wants to find very tall people to be on its Olympic basketball team and strike a blow against western imperialism. Out of a pool of 108 people who are the right age and gender, how many are they likely to find who are over 225 cm (7 feet 4 inches) in height? Figure g gives a close-up of the "tail" of the distribution shown previously in figure f.

g / A close-up of the righthand tail of the distribution shown in the figure f.

The shaded area under the curve represents the probability that a given person is tall enough. Each rectangle represents a probability of 0.2 10-7 cm-1 1 cm = 2 10-9. There are about 35 rectangles covered by the shaded area, so the probability of having a height greater than 225 cm is 710-8 , or just under one in ten million. Using the rule for calculating averages, the average, or expected number of people this tall is (108) (7 10-8) = 7.

Last Update: 2009-06-21