The scores from a state standardized test have a mean of 80 and a standard deviation of 10. The distribution ofthe scores is roughly bell shaped. Use the Empirical Rule to find the percentage of scores that lie between 60and 80.
A) 47.5%
B) 68%
C) 34%
D) 95%

Question

Quizplus · Accepted Answer

The Empirical Rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean. Since the mean is 80 and the standard deviation is 10, the range from 70 to 90 (one standard deviation below and above the mean) contains about 68% of the scores. The question asks for the percentage between 60 and 80, which is two standard deviations below the mean to the mean itself. This range covers half of the 68% (from 70 to 80) plus half of the next 27% (from 60 to 70, since 95% of the data falls within two standard deviations, leaving 95%-68%=27% for the two tails beyond one standard deviation). Half of 68% is 34%, and half of 27% is 13.5%, so adding these gives 34% + 13.5% = 47.5%.

The Scores from a State Standardized Test Have a Mean