Recall that the heights of WNBA players are Normally distributed with a mean of 72 in. and a standard deviationof 2 in., and that NBA players’ heights have a mean of 79 in. and a standard deviation of 3 in. Obviously, NBA players are taller on average than WNBA players. However, it is possible to find a WNBA player that is taller than an NBA player. Likewise, it is possible to find an NBA player shorter than a WNBA player.
The histograms below simulate the heights of 100 WNBA players and 100 NBA players. You are only given the height of the chosen player. How likely is it that you mistake a WNBA player for an NBA player based only on the player's height?