Final answer:
The percentage of seniors who scored between 271 and 751 on the SAT Mathematics section in 2015 cannot be determined without the specific mean and standard deviation for that year. However, a student with an SAT score of 720 has a z-score of approximately 1.74, indicating they scored well above the mean. An SAT math score of 692.5 is 1.5 standard deviations above the mean, which is also above average.
Step-by-step explanation:
To answer the question regarding the percentage of seniors who scored between 271 and 751 on the SAT Mathematics section in 2015, we would need the distribution mean and standard deviation for that year, which are not provided in the question. However, we can answer the sample questions with the given data for other years.
Calculating a z-score for an SAT score
To calculate the z-score for an SAT score of 720 using a mean (μ) of 520 and a standard deviation (σ) of 115:
z = (X - μ) / σ
z = (720 - 520) / 115 ≈ 1.74
This z-score indicates that an SAT score of 720 is approximately 1.74 standard deviations above the mean.
Finding an SAT score a specific number of standard deviations above the mean
An SAT math score that is 1.5 standard deviations above the mean of 520 can be calculated as follows:
Score = μ + (z × σ)
Score = 520 + (1.5 × 115) ≈ 692.5
This score is considered to be considerably higher than the average.