A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was 507 with a margin of error of 12 . Write a confidence interval for the true mean SAT score of the graduating high school seniors.
attempt 1 out of 2

Step 1 ：A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was 507 with a margin of error of 12 .

Step 2 ：A confidence interval is a range of values, derived from a statistical calculation, that is likely to contain an unknown population parameter. In this case, we are trying to find the confidence interval for the true mean SAT score of the graduating high school seniors.

Step 3 ：The mean SAT score is given as 507 and the margin of error is 12. The confidence interval can be calculated as the mean plus or minus the margin of error.

Step 4 ：\(\text{mean} = 507\)

Step 5 ：\(\text{margin of error} = 12\)

Step 6 ：\(\text{lower bound} = \text{mean} - \text{margin of error} = 507 - 12 = 495\)

Step 7 ：\(\text{upper bound} = \text{mean} + \text{margin of error} = 507 + 12 = 519\)

Step 8 ：Final Answer: The confidence interval for the true mean SAT score of the graduating high school seniors is \(\boxed{(495, 519)}\).