From the mid-1960s to the early 1990s, there was a slow but steady decline in SAT scores. For example, take the Verbal SAT. The average in 1967 was about 543; by 1994, the average was down to about 499. However, the SD stayed close to 110. The drop in averages has a large effect on the tails of the distribution.

(a) Estimate the percentage of students scoring over 700 in 1967.

(b) Estimate the percentage of students scoring over 700 in 1994.

You may assume that the histograms follow the normal curve.

Comments. SAT scores range from 200 to 800. It does not seem that the SAT was getting harder. Most of the decline in the 1960s is thought to result from changes in the population of students taking the test. The decline in the 1970s cannot be explained that way. From 1994 to 2005, scores generally increased.

The test was re-normalized in 1996, which complicates the interpretation; the averages mentioned above were converted to the new scale.⁴ p-968