In a recent year, the total scores for a certain handardized test were normally distributed, with a mean of 500 and a standard deviation of 10.5 . Answer parts (a)-(d) below. (a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 489 . The probability that a randomly selected medical student who took the test had a total score that was less than 489 is (Round to four decimal places as needed.)

Step 1 ：Given that the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.5.

Step 2 ：We are asked to find the probability that a randomly selected medical student who took the test had a total score that was less than 489.

Step 3 ：To solve this problem, we need to use the concept of Z-score in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.

Step 4 ：In this case, we need to calculate the Z-score for the score 489, and then find the probability that a score is less than this Z-score.

Step 5 ：First, calculate the Z-score using the formula \(Z = \frac{X - \mu}{\sigma}\), where \(X\) is the score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step 6 ：Substitute the given values into the formula: \(Z = \frac{489 - 500}{10.5} = -1.0476190476190477\).

Step 7 ：Next, we find the probability that a score is less than this Z-score. The probability is approximately 0.14740707903152722.

Step 8 ：Final Answer: The probability that a randomly selected medical student who took the test had a total score that was less than 489 is approximately \(\boxed{0.1474}\).