The dispersion of serum protein-bound iodine levels in euthyroid subjects does not allow a normal curve of distribution. Therefore, the mean ± 2 standard deviations does not define the central 95% of a "normal" population for this test. The logarithmic transformation provides a reasonably good fit to the normal distribution curve and allows the calculation of the central 95% of the values. In this study the limits of the central 95% of values were 3.4 to 8.2μg/100 ml.
Jerald C. Nelson, Elizabeth Haynes, Rodney Willard, Jan Kuzma. The Distribution of Euthyroid Serum Protein-Bound Iodine Levels. JAMA. 1971;216(10):1639–1641. doi:10.1001/jama.1971.03180360085017