The distribution of weights of female college cross-country runners is approximately normal with mean 122 pounds and standard deviation 8 pounds. Which of the following is closest to the percent of the runners who weight between 114 pounds and 138 pounds?

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We can find the \(z\)-scores that correspond to each value. In this case, the 114 pounds marks one standard deviation below the mean (\(z=-1\)) and 138 pounds marks two standard deviations above the mean (\(z=2\)). In the table, we find the corresponding values of 0.1587 and 0.9772. Subtracting these two values result in the area under the curve, and the probability:

$$ 0.9772-0.1587 = 0.8185 \approx \boxed{82\%} $$