Final answer:
A z-score of 2.38 indicates a test score 2.38 standard deviations above the mean. A z-score of -1 would place a student's score around the 16th percentile under a Nearly Normal Condition.
Step-by-step explanation:
If you received a z-score of 2.38 on an exam, it means that your score was 2.38 standard deviations above the mean score of the class. In a Nearly Normal Condition, which is typically the case for a standard normal distribution, a z-score of -1 implies that your friend's grade was below the mean. If we apply the empirical rule, sometimes referred to as the 68-95-99.7 rule, we know that approximately 68% of the values lie within one standard deviation of the mean (z-scores -1 to 1). As such, a z-score of -1 would roughly correspond to the 16th percentile, meaning about 16% of the class scored lower than your friend.
If the grades satisfy the Nearly Normal Condition, about 15.87% of the class scored lower than your friend. This can be determined by looking up the z-score of -1 in the standard normal distribution table, which corresponds to the area to the left of -1.