Step 1 :Calculate the Z-score using the formula: \(Z = \frac{X - \mu}{\sigma}\)
Step 2 :Substitute the given values into the formula: \(Z = \frac{489 - 500}{10.8} = -1.0185\)
Step 3 :The Z-score tells us that a score of 489 is approximately 1.0185 standard deviations below the mean.
Step 4 :Find the probability that corresponds to this Z-score by looking up the Z-score in a standard normal distribution table, or using a calculator or software that can calculate it.
Step 5 :The probability that corresponds to a Z-score of -1.0185 is approximately 0.1545.
Step 6 :So, the probability that a randomly selected medical student who took the test had a total score that was less than 489 is approximately 0.1545, or 15.45%.
Step 7 :\(\boxed{0.1545}\) is the final answer.