Final answer:
The question relates to calculating a z-score for an SAT math score and determining the score at a certain number of standard deviations above the mean in a normal distribution. The subject of this question relates to statistics, specifically to the concept of z-scores and the properties of a normal distribution in the context of standardized test scores like the SAT.
Step-by-step explanation:
The subject of this question relates to statistics, specifically to the concept of z-scores and the properties of a normal distribution in the context of standardized test scores like the SAT.
a. To calculate the z-score for an SAT score of 720, you use the formula z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (720 - 520) / 115 ≈ 1.74. This z-score means the score of 720 is approximately 1.74 standard deviations above the mean score of the SAT.
b. The SAT math score that is 1.5 standard deviations above the mean can be found by taking the mean score and adding 1.5 times the standard deviation: 520 + 1.5(115) ≈ 692.5. This indicates that a score of 692.5 is higher than the majority of test-takers' scores, as it is 1.5 standard deviations above the mean.