Average Math and Reading SAT Scores

The average Math and Reading SAT score in 2014 was 1010. Suppose the distribution of scores is approximately bell shaped and the standard deviation is approximately 86.a) Within what boundaries would you expect 68% of the scores?b) What percentage of scores would you expect to be above 1182?

Solution:

a)I would expect 68% of the data values to fall within 1 standard deviation of the mean.

The upper boundary will be____________________________

The lower boundary will be____________________________

Thus, I expect 68% of the data values to be between _______________.

b)To find the percentage of scores above 1182, find the number of standard deviations the value is from the mean.

1182 = 1010 + (number of standard deviations from the mean) * 86

172 = (number of standard deviations from the mean) * 86

2 = number of standard deviations from the mean

By the Empirical Rule, we expect 95% of the data within 2 standard deviations of the mean.So, 5% is evenly split between the amount of data values above and below the mean.That means 2.5% of the data is expected to be above 1182.