Use the Empirical Rule to Describe Data That Are Bell Shaped
-The scores from a state standardized test have a mean of 80 and a standard deviation of 10 . The distribution of the scores is roughly bell shaped. Use the Empirical Rule to find the percentage of scores that lie between 60 and 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, 95% within two standard deviations, and 99.7% within three standard deviations. The range from 60 to 80 is one standard deviation below to the mean (80 - 10 = 70, 80 - 20 = 60). Therefore, about 34% of the scores lie below 70 (one standard deviation below the mean), and about 34% lie between 70 and 80, totaling approximately 68% for the range from 60 to 80. However, since the question asks for the range from 60 to 80, we consider only the portion from 70 to 80 (34%) and the portion below 70 (another 34%), totaling 68%. The correct interpretation for the range specifically from 60 to 80 is half of the data, since it covers from the mean to one standard deviation below, which is approximately 50% of the data. My initial explanation mistakenly applied the Empirical Rule in a way that suggested a direct sum of percentages for two segments, which was incorrect in this context. The correct answer should reflect the percentage of scores within one standard deviation below the mean, which is indeed about 50% of the distribution, not 68% as previously stated. Given the options provided and the correct understanding of the Empirical Rule, none of the choices directly match the accurate explanation. The closest interpretation based on the standard application of the Empirical Rule would suggest looking for an option that represents about half of the data within one standard deviation, but given the options and the misinterpretation in my explanation, there seems to be a misunderstanding in applying the rule to this specific question.

Use the Empirical Rule to Describe Data That Are Bell 47.5%47.5 \%47.5%

Use the Empirical Rule to Describe Data That Are Bell $47.5 \%$