.
Heights of men on a baseball team have a bell-shaped distribution with a mean of 172 cm
and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage
of the men between the following values?
a. 154 cm and 190 cm
b. 160 cm and 184 cm
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(a) Interval [154,190] is three standard deviations from the mean.
So, the empirical rule for 3 standard deviations is applicable in this case,
giving the ANSWER that the height of approximately 99.7% of the men is in this interval.
(b) Interval [160,184] is two standard deviations from the mean.
So, the empirical rule for 2 standard deviations is applicable in this case,
giving the ANSWER that the height of approximately 95% of the men is in this interval.