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M414 Chapter 3 Worksheet 3 Empirical Rule and Normal Distribution Name Date Period In a normal distribution, what percent of the values lie: 1. below the mean? 2. above the mean? 3. within one standard.

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Filling out the M414 Chapter 3 Worksheet 3 requires careful attention to detail and an understanding of normal distribution concepts. This guide will provide step-by-step instructions to help you complete the form accurately and efficiently.

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  4. For questions about percentages in a normal distribution, provide the appropriate values in the fields presented, specifying the percentage below the mean, above the mean, and within specified standard deviations.
  5. For each data set provided (for example, the students' test scores), carefully analyze the statistics and calculate answers for the related questions, recording your answers in the provided spaces.
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scored between 60 and 70? 13.5+ 34=47.5%.

Answer: The mean SAT score is 500. 68% of students score between 500–100=400 and 500+100=600. The remaining 32% score outside of this range. So (16+34+34)% = 84% score 600 or lower.

Answer and Explanation: About 68% of the students scored between 400 and 600.

So 68% + 16% = 84% of SAT scores are above 400. (b) What percentage of SAT scores are above 500? Since 500 is the median, 50% of SAT scores are above it.

So because of symmetry 50% of the test scores fall in the area above the mean and 50% of the test scores fall in the area below the mean. We know from part b that the percentage from 65 to 75 is 47.5%.

Empirical Rule or 68-95-99.7% Rule Approximately 68% of the data fall within one standard deviation of the mean. Approximately 95% of the data fall within two standard deviations of the mean. Approximately 99.7% of the data fall within three standard deviations of the mean.

The proportion of students with SAT scores less than 400 is approximately 0.1587. b. The proportion of students with SAT scores greater than 650 is approximately 0.0918.

Expert-Verified Answer. Using the normal distribution, it is found that 58.97% of students would be expected to score between 400 and 590.

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