Heights of men on a baseball team have a bell-shaped distribution with a mean of 186 cm and a standard deviation of 8 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?
a. 162 cm and 210 cm
b. 178 cm and 194 cm
The empirical rule says that for data sets having a distribution that is approximately bell-shaped, the following properties apply.
a. the values are 3 standard deviations away from the mean, so the percentage of values within that range will be 99.7%
b. by similar reasoning the values are 1 standard deviation away from the mean -- or will contain 68% of the values.
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