For example, many psychological and educational tests are purposely constructed to follow a normal distribution. The purpose of T-scores is primarily to get rid of the negative values and decimal numbers associated with Z-scores.
A common example would be the Wechsler Adult Intelligence Scale (WAIS) which uses
T = 100 + 10*Z
where the mean is 100 (not 50) and the values of T are rounded to whole numbers.