Final answer:
To compute the z-score for an SAT score of 1150, with a mean of 520 and standard deviation of 115, the student's score is approximately 5.4783 standard deviations above the mean, indicating a performance significantly better than average.
Step-by-step explanation:
The z-score is a statistical measurement that describes a value's relationship to the mean of a group of values.
To calculate a z-score we use the formula z = (X - μ) / σ, where X is the score in question, μ is the mean, and σ is the standard deviation.
Given that the mean SAT score is 520 with a standard deviation of 115, a student with an SAT Score of 1150 would have a z-score calculated as follows:
z = (1150 - 520) / 115
z = 630 / 115
z = 5.4783
This means the student's score is approximately 5.4783 standard deviations above the mean.
Interpreting this z-score indicates that the student's performance on the SAT was significantly better than the average test taker.