According to a recent report from the U.S. National Center for Health Statistics, for males aged 24-34, 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 call cumulative percentages.
(a) Between what two heights is the median of the heights of young men ages 24-34? Explain.
(b) Nearly all of the heights fall between 60 inches and 80 inches with fewer than 1% of heights falling outside this range. If the heights are approximately bell-shaped, give a rough approximation for the standard deviation of the heights. Explain your reasoning.