**Normatively Distributed Data Set Explanation**In a normally distributed data set with a mean of 31, 95% of the data falls between 27.4 and 34.6. The key question is: what would be the standard deviation of that data set?### Homework Help Resources:- **4VG. Empirical Rule with examples** [Link: 4VG Empirical Rule with examples (4:38)]- **4DE. Standard scores and the Empirical Rule** [Link: 4DE Standard scores and the Empirical Rule (DOCX)]### Multiple Choice Options:- [ ] 2.6- [ ] 7.6- [ ] 1.8- [ ] 3.1### Detailed Explanation:In a normally distributed data set, the Empirical Rule states that approximately 95% of the data falls within two standard deviations from the mean. This implies:Mean ± 2 * (Standard Deviation) = Lower Bound and Upper BoundGiven:- Mean (μ) = 31- Lower Bound = 27.4- Upper Bound = 34.6Using the Empirical Rule:- 31 - 27.4 = 3.6- 34.6 - 31 = 3.6Therefore, 2 * (Standard Deviation) = 3.6So, Standard Deviation = 3.6 / 2 = 1.8### Correct Answer:- [ ] 2.6- [ ] 7.6- [x] 1.8- [ ] 3.1

To find the standard deviation of a normally distributed data set, given the mean and the range…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 60 ounces and a standard deviation of 3 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule (see image below). Do not use normalcdf on your calculator. Suggestion: sketch the distribution in order to answer these questions. a) 99.7% of the widget weights lie between b) What percentage of the widget weights lie between 57 and 69 ounces? c) What percentage of the widget weights lie above 54 ? 0.15% -3s 2.35% -25 13.5% -1s 34% 34% 1s 13.5% 2s 2.35% 3s and 0.15% % %
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Lecture(10.8): The Peabody Picture Vocabulary Test has a standard score mean of 100 and a standard deviation of 15. You tested a class of grade 2 students wonderinf if these scores would be different from the population. After testing this hypotheses you decided to continue looking at this data to determine if there are any group differences based on birth order. You group the children the on whether they are the oldest chlid, middle child, or the youngest child. Here is the data based on grouped information. Oldest child: 87 84 98 104 106 91 96 92 Middle child: 65 74 62 60 73 64 71 78 Youngest child: 115 84 85 83 95 94 108 102 89 Test the hypotheses at (alpha=0.05) level of signifance using the 5 step procedure.Make sure to clearly state the null and alternative hypotheses.Round your answer to 2 decimal. You are encouraged to use the following table to help you…
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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 37 ounces and a standard deviation of 6 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule (see image below). Do not use normalcdf on your calculator. Suggestion: sketch the distribution in order to answer these questions. a) 99.7% of the widget weights lie between b) What percentage of the widget weights lie between 25 and 55 ounces? c) What percentage of the widget weights lie below 43 ? 0.15% -3s 2.35% -25 13.5% 34% 34% Submit Question 1s 13.5% 2s 2.35% 35 0.15% Question Help: Video Written Example Message instructor and % %
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z Scores LeBron James, one of the most successful basketball players of all time, has a height of 6 feet 8 inches, or 203 cm. Based on statistics from Data Set 1 “Body Data” in Appendix B, his height converts to the z score of 4.07. How many standard deviations is his height above the mean?
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In a normally distributed data set a mean of 31 where 95% of the data fall between 27.4 and 34.6, what would be the standard deviation of that data set? Homework Help: 4VG. Empirical Rule with examples (4:38) 4DE. Standard scores and the Empirical Rule (DOCX) O 2.6 O 7.6 O 1.8 3.1