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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 50 ounces and a standard deviation of 4 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) 95% of the widget weights lie between and b) What percentage of the widget weights lie between 46 and 58 ounces? c) What poscentage of the widget weights lie below 62 ?

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 50 ounces and a standard deviation of 4 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) 95% of the widget weights lie between and b) What percentage of the widget weights lie between 46 and 58 ounces? c) What poscentage of the widget weights lie below 62 ?

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
Problem 1P
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### Distribution of Widget Weights **Context:** The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 50 ounces and a standard deviation of 4 ounces. **Instructions:** Use the Standard Deviation Rule, also known as the Empirical Rule, to answer the questions below. Do not use a calculator. Sketching the distribution may aid in understanding. **Questions:** a) **95% of the widget weights lie between** [ ] and [ ] ounces. b) **What percentage of the widget weights lie between 46 and 58 ounces?** [ ] % c) **What percentage of the widget weights lie below 62?** [ ] % --- ### Explanation of the Diagram The diagram represents a bell-shaped curve depicting the normal distribution of widget weights. It uses the Empirical Rule to show the distribution of data across standard deviations from the mean: - **Mean (μ):** 50 ounces - **Standard Deviation (σ):** 4 ounces **Sections of the Curve:** - **34%** of the data lies between +1σ and -1σ from the mean. - **13.5%** of the data lies between +2σ and +1σ, and -2σ and -1σ from the mean. - **2.35%** of the data lies between +3σ and +2σ, and -3σ and -2σ from the mean. - **0.15%** of the data lies beyond +3σ and -3σ. The image clearly articulates each zone with different colors to indicate the percentages of data within one, two, and three standard deviations from the mean. This visualization helps in comprehensively understanding the distribution and application of the Empirical Rule in this context.
Transcribed Image Text:### Distribution of Widget Weights **Context:** The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 50 ounces and a standard deviation of 4 ounces. **Instructions:** Use the Standard Deviation Rule, also known as the Empirical Rule, to answer the questions below. Do not use a calculator. Sketching the distribution may aid in understanding. **Questions:** a) **95% of the widget weights lie between** [ ] and [ ] ounces. b) **What percentage of the widget weights lie between 46 and 58 ounces?** [ ] % c) **What percentage of the widget weights lie below 62?** [ ] % --- ### Explanation of the Diagram The diagram represents a bell-shaped curve depicting the normal distribution of widget weights. It uses the Empirical Rule to show the distribution of data across standard deviations from the mean: - **Mean (μ):** 50 ounces - **Standard Deviation (σ):** 4 ounces **Sections of the Curve:** - **34%** of the data lies between +1σ and -1σ from the mean. - **13.5%** of the data lies between +2σ and +1σ, and -2σ and -1σ from the mean. - **2.35%** of the data lies between +3σ and +2σ, and -3σ and -2σ from the mean. - **0.15%** of the data lies beyond +3σ and -3σ. The image clearly articulates each zone with different colors to indicate the percentages of data within one, two, and three standard deviations from the mean. This visualization helps in comprehensively understanding the distribution and application of the Empirical Rule in this context.
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