Asked by Fahad Hashmi on Jun 16, 2024
Verified
In a time study, conducted at a manufacturing plant, the length of time to complete a specified operation is measured for each on n = 40 workers. The mean and standard deviation are found to be 15.2 and 1.40, respectively.
a. Describe the sample data using the Empirical Rule.
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b. Describe the sample data using Tchebysheff's Theorem.
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Empirical Rule
A statistical rule stating that for a normally distributed dataset, about 68% of values fall within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean.
Tchebysheff's Theorem
A mathematical formula that determines the minimum proportion of values that lie within a specified number of standard deviations from the mean, for any distribution.
- Gain familiarity with the applications and limitations of statistical norms (Empirical Rule, Tchebysheff's Theorem) in presenting data.
- Execute applications of the Empirical Rule and Tchebysheff's Theorem within theoretical and practical scenarios.
- Provide an explanation of how to compute variance and standard deviation, and their value in data analytic practices.
Verified Answer
DS
Daniel Salas MoraJun 18, 2024
Final Answer :
If the distribution of measurements is mound-shaped, you can apply the Empirical Rule and expect approximately 68% of the measurements to fall into the interval from 13.8 to 16.6, approximately 95% to fall into the interval from 12.4 to 18.0, and all or almost all to fall into the interval from 11.0 to 19.4.; If you doubt that the distribution of measurements is mound-shaped, or if you wish for some other reason to be conservative, you can apply Tchebysheff's Theorem and be absolutely certain of your statements. Tchebysheff's Theorem tells you that at least 3/4 of the measurements fall into the interval from 12.4 to 18.0 and at least 8/9 into the interval from 11.0 to 19.4.
Learning Objectives
- Gain familiarity with the applications and limitations of statistical norms (Empirical Rule, Tchebysheff's Theorem) in presenting data.
- Execute applications of the Empirical Rule and Tchebysheff's Theorem within theoretical and practical scenarios.
- Provide an explanation of how to compute variance and standard deviation, and their value in data analytic practices.