When z is a whole number, the Empirical rule can be used to estimate the appropriate area
under the normal curve. What happens if z is not a whole number? Suppose we needed to know
the percent of recruits with heights between 175cm and 185cm. Using the z equation, we would
get z = X - u = 185 - 175 = 10 = 1.67. There is no value in the Empirical rule for 1.67
deviations above the mean. Interpolating (finding the value 2/3 of the way between 1 and 2
standard deviations) would cause a large error because the normal curve is not a straight line.
Computing the area using a pocket calculator would be a lengthy and tedious task. The easiest
and most common method is to look up the area in a table. Such a table, titled AREAS UNDER
THE STANDARD NORMAL CURVE, is on the next page.