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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

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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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**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 Bound Given: - Mean (μ) = 31 - Lower Bound = 27.4 - Upper Bound = 34.6 Using the Empirical Rule: - 31 - 27.4 = 3.6 - 34.6 - 31 = 3.6 Therefore, 2 * (Standard Deviation) = 3.6 So, Standard Deviation = 3.6 / 2 = 1.8 ### Correct Answer: - [ ] 2.6 - [ ] 7.6 - [x] 1.8 - [ ] 3.1
Transcribed Image Text:**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 Bound Given: - Mean (μ) = 31 - Lower Bound = 27.4 - Upper Bound = 34.6 Using the Empirical Rule: - 31 - 27.4 = 3.6 - 34.6 - 31 = 3.6 Therefore, 2 * (Standard Deviation) = 3.6 So, Standard Deviation = 3.6 / 2 = 1.8 ### Correct Answer: - [ ] 2.6 - [ ] 7.6 - [x] 1.8 - [ ] 3.1
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