In class, we discussed what fraction of 7-foot or taller males of an appropriate age play in the NBA. This exercise demonstrates the sensitivity of such calculations to underlying assumptions.
a. There are 20 US-born 7-footers who have played at least one game in the NBA in the current 2013-2014 season. There are X total 7-footers between the ages of 20 and 35 living in the US. Estimate X under the following assumptions:
• There are 316,710,000 total people living in the US
• 49.22% of people living in the US are male.
• 1 of all males are between the ages of 20 and 35. 4
• The average height of a male is 5 feet, 10 inches. • The standard deviation of male height is 3 inches
b. Repeat part a, but now assume that the standard deviation of male height is 3.2 inches. How does this change your estimate of the fraction of all 7-footers who currently play in the NBA (20)?
c. Repeat part a, but now assume that the standard deviation of male height is 3.4 inches. How does this change your estimate of the fraction of all 7-footers who play in the NBA?