According to a recent report from the U.S. National Center for Health Statistics, for males
aged 25–34 years, 2% of their heights are 64 inches or less, 8% are 66 inches or less, 27% are 68 inches or less, 39% are 69 inches or less, 54% are 70 inches or less, 68% are 71 inches or less, 80% are 72 inches or less, 93% are 74 inches or less, and 98% are 76 inches or less. These are called cumulative percentages.
a. Which category has the median height? Explain why.
b. Nearly all the heights fall between 60 and 80 inches, with fewer than 1% falling outside that range. If the heights are approximately bell-shaped, give a rough approximation for the standard deviation of the heights. Explain your reasoning.