Question 17 of 33 The Normal distribution with mean \( \mu=500.9 \) and standard deviation \( \sigma=10.6 \) is a good description of the total score on the Medical College Admission Test (MCAT). This is a continuous probability model for the score of a randomly chosen student. Call the score of a randomly chosen student \( X \) for short. Side-by-Side (b) Use Table A to find the probability of the event "the student chosen has a score of 510 or higher." Give your answer to four decimal places. probability: \( \square \)

To find the probability that a randomly chosen student has a score of 510 or higher, we first need to standardize the score using the formula for the standard normal variable \( Z \): \[ Z = \frac{X - \mu}{\sigma} = \frac{510 - 500.9}{10.6} \approx 0.1043. \] Next, we can look up this Z-score in the standard normal distribution table (Table A) or use a calculator that gives cumulative probabilities. Using the Z-table, we can find that the probability \( P(Z < 0.1043) \approx 0.5410 \). To find the probability of scoring 510 or higher, we need to calculate: \[ P(X \geq 510) = 1 - P(Z < 0.1043) = 1 - 0.5410 = 0.4590. \] Thus, the probability that a randomly chosen student has a score of 510 or higher is approximately \( 0.4590 \).