Final answer:
To be in the top 17% of the scores on the physics exam, a student would need to score at least 82.43, using the z-score for the 83rd percentile which is approximately 0.95.
Step-by-step explanation:
To find the minimum score a student would need to earn to be in the top 17 percent of scores in a normally distributed set with a mean of 81 and a standard deviation of 1.5, we need to find the z-score that correlates with the top 17% of the distribution.
Consulting a standard normal distribution (z-score) table or using a statistical calculator, we find that the z-score corresponding to the top 17% (or the 83rd percentile, since 100% - 17% = 83%) is approximately 0.95.
Using the z-score formula:
- Z = (X - mean) / standard deviation
- X = Z * standard deviation + mean
- X = 0.95 * 1.5 + 81
- X = 1.425 + 81
- X = 82.43
Therefore, a student would need to score at least 82.43 to be in the top 17 percent of scores on this physics exam.