Mayreni Nunez
11/08/23 9:16 PM
ion 5.2
Question 5, 5.2.9-T
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In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.8. 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 $\square$.
(Round to four decimal places as needed.)

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.