Question

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.

Answer 1

a) 7.68%

b) 3.38%

Explanation:

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

The probability that a student scored over 700 in 1967 equals the area under the Normal curve with mean 543 and standard deviation 110 to the right of 700.

In Excel this value is found with the formula

=1-NORMDIST(700,543,110,1)

and in OpenOffice Calc

=1-NORMDIST(700;543;110;1)

(NORMDIST(700;543;110;1) gives the area to the left of 700, so 1-NORMDIST(700;543;110;1) gives the area to the right of 700)

and equals 0.07675

So, the percentage of students scoring over 700 in 1967 was 7.68%

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

The probability that a student scored over 700 in 1994 equals the area under the Normal curve with mean 499 and standard deviation 110 to the right of 700.

In Excel this value is found with the formula

=1-NORMDIST(700,499,110,1)

and in OpenOffice Calc

=1-NORMDIST(700;499;110;1)

and equals 0.03383

So, the percentage of students scoring over 700 in 1994 was 3.38%