Final answer:
To predict the final exam score for a student who scored a 66 on the third exam, we need to calculate the z-score for the score, which can then be used to find the corresponding percentile. Based on the percentile, we can make a prediction about the final exam score.
Step-by-step explanation:
To predict the final exam score for a student who scored a 66 on the third exam, we can use the information provided about the college entrance exam scores. The scores follow an approximate normal distribution with a mean of 52 and a standard deviation of 11. We can calculate the z-score for the student's score using the formula z = (x - µ) / σ, where x is the student's score, µ is the mean, and σ is the standard deviation.
Let's calculate the z-score for a score of 66:
z = (66 - 52) / 11
z ≈ 1.27
Next, we can use the z-score to find the corresponding percentile. We can look up the percentile in a standard normal distribution table or use a calculator to find that a z-score of 1.27 corresponds to a percentile of approximately 90.77%. This means that the student's score of 66 is higher than about 90.77% of the scores on the college entrance exam.
Based on this information, we can predict that the student's final exam score will be higher than their third exam score of 66, but the exact score cannot be determined without further information.