In 1995, more than 1.1 million students in the U.S. took the SAT. On the mathematics section, the mean =507, s=112 (standard deviation). Students receive scores rounded to the nearest 10. What is the interval of student scores that lie within one standard deviation of the mean?
That would be the interval from 507-112 = 395, to 507+112 = 619. If you round both ends of that interval to the nearest 10, it would be 400 to 620.
To calculate the interval of student scores that lie within one standard deviation of the mean, you need to subtract the standard deviation from the mean to find the lower bound and add the standard deviation to the mean to find the upper bound.
Given:
Mean = 507
Standard Deviation (s) = 112
To find the lower bound:
Lower Bound = Mean - Standard Deviation
Lower Bound = 507 - 112
Lower Bound = 395
To find the upper bound:
Upper Bound = Mean + Standard Deviation
Upper Bound = 507 + 112
Upper Bound = 619
Therefore, the interval of student scores that lie within one standard deviation of the mean is from 395 to 619.
Since student scores are rounded to the nearest 10, you need to round the lower and upper bounds to the nearest 10:
Rounded Lower Bound = 400
Rounded Upper Bound = 620
Therefore, the interval of student scores that lie within one standard deviation of the mean, rounded to the nearest 10, is from 400 to 620.