Final answer:
A score of 1.5 standard deviations below the mean on a standardized test corresponds to a z-score of -1.5, which places you at approximately the 6.68th percentile, indicating that you scored better than about 6.68% of test takers.
Step-by-step explanation:
If you have a score on a standardized test that puts you 1.5 standard deviations below the mean, you are looking to find your percentile score based on a z-score of -1.5. In a standard normal distribution, a z-score represents how many standard deviations a value is from the mean, where the mean z-score is 0 and the standard deviation is 1. Percentiles correspond to the area under the normal curve to the left of the z-score, or in other words, they represent the percentage of scores that fall below a given score. To determine the percentile for a z-score of -1.5, you can use a z-score table or a standard normal distribution calculator. Typically, a z-score of -1.5 corresponds to approximately the 6.68th percentile. This means that if your score is 1.5 standard deviations below the mean, you scored better than about 6.68% of the population that took the test.