suppose that shoe sizes of american women have a bell-shaped distribution with a mean of 8.42 and a standard deviation of 1.52. using the empirical rule, what percentage of american women have shoe sizes that are between 6.9 and 9.94? when the distribution of a set of data is approximately bell-shaped, the empirical rule can be used to estimate the percentage of values that lie within a few standard deviations of the mean. we need to know how many standard deviations from the mean 6.9 and 9.94 are. by subtracting, we can find how far each of these figures is from the mean. then, dividing by the standard deviation, we can convert these differences into numbers of standard deviations. note: this is the same calculation that is used to find the standard score, or z-score, of a data value.
