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54. Empirical Rule OK? The following histogram presents a data set with a mean of 62 and a standard deviation of 17. Is it appropriate to use the Empirical Rule to approximate the proportion of the data between 45 and 79? If so, find the approximation. If not, explain why not. Frequency 20 15 0 5 20 30 40 50 60 70 80 90

54. Empirical Rule OK? The following histogram presents a data set with a mean of 62 and a standard deviation of 17. Is it appropriate to use the Empirical Rule to approximate the proportion of the data between 45 and 79? If so, find the approximation. If not, explain why not. Frequency 20 15 0 5 20 30 40 50 60 70 80 90

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Empirical Rule Analysis #### Question: **54. Empirical Rule OK?** The following histogram presents a data set with a mean of 62 and a standard deviation of 17. Is it appropriate to use the Empirical Rule to approximate the proportion of the data between 45 and 79? If so, find the approximation. If not, explain why not. #### Explanation of the Histogram: The histogram below visually represents the frequency distribution of a data set: - **X-axis (Horizontal):** This axis represents the data values, divided into intervals: - The intervals are: 20-30, 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100. - **Y-axis (Vertical):** This axis represents the frequency of data points within each interval: - Frequencies range from 0 to 20. **Bars Representation:** - The height of each bar corresponds to the frequency of data points within the respective interval. - The interval 20-30 has a frequency of about 5. - The interval 30-40 has a frequency of about 8. - The interval 40-50 has a frequency of about 10. - The interval 50-60 has a frequency of about 12. - The interval 60-70 has a frequency of about 15. - The interval 70-80 has a frequency of about 18. - The interval 80-90 has a frequency of about 14. #### Analysis: To determine if the Empirical Rule (68-95-99.7 rule) is appropriate, we should consider the shape of the histogram. The Empirical Rule applies to data that follows a normal distribution (approximately bell-shaped curve). - **Mean (μ):** 62 - **Standard Deviation (σ):** 17 - **Empirical Rule Intervals:** - 1σ (68%): μ ± σ ⇒ 62 ± 17 ⇒ 45 to 79 In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. #### Conclusion: Based on the histogram, the data does not appear to follow a perfect bell curve (normal distribution), but it somewhat resembles one. If the shape approximation is close enough, the Empirical Rule might still provide a
Transcribed Image Text:### Empirical Rule Analysis #### Question: **54. Empirical Rule OK?** The following histogram presents a data set with a mean of 62 and a standard deviation of 17. Is it appropriate to use the Empirical Rule to approximate the proportion of the data between 45 and 79? If so, find the approximation. If not, explain why not. #### Explanation of the Histogram: The histogram below visually represents the frequency distribution of a data set: - **X-axis (Horizontal):** This axis represents the data values, divided into intervals: - The intervals are: 20-30, 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100. - **Y-axis (Vertical):** This axis represents the frequency of data points within each interval: - Frequencies range from 0 to 20. **Bars Representation:** - The height of each bar corresponds to the frequency of data points within the respective interval. - The interval 20-30 has a frequency of about 5. - The interval 30-40 has a frequency of about 8. - The interval 40-50 has a frequency of about 10. - The interval 50-60 has a frequency of about 12. - The interval 60-70 has a frequency of about 15. - The interval 70-80 has a frequency of about 18. - The interval 80-90 has a frequency of about 14. #### Analysis: To determine if the Empirical Rule (68-95-99.7 rule) is appropriate, we should consider the shape of the histogram. The Empirical Rule applies to data that follows a normal distribution (approximately bell-shaped curve). - **Mean (μ):** 62 - **Standard Deviation (σ):** 17 - **Empirical Rule Intervals:** - 1σ (68%): μ ± σ ⇒ 62 ± 17 ⇒ 45 to 79 In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. #### Conclusion: Based on the histogram, the data does not appear to follow a perfect bell curve (normal distribution), but it somewhat resembles one. If the shape approximation is close enough, the Empirical Rule might still provide a
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