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The Acme Company manufactures widgets. The distribution of widget weights is bell- shaped. The widget weights have a mean of 43 ounces and a standard deviation of 8 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 35 and 59 ounces? % c) What percentage of the widget weights lie above 19? 34% 34% 2.35% 0.15% -3s -2s 13.5% - -1s 0 1s 13.5% 2s 2.35% 3s 0.15%

The Acme Company manufactures widgets. The distribution of widget weights is bell- shaped. The widget weights have a mean of 43 ounces and a standard deviation of 8 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 35 and 59 ounces? % c) What percentage of the widget weights lie above 19? 34% 34% 2.35% 0.15% -3s -2s 13.5% - -1s 0 1s 13.5% 2s 2.35% 3s 0.15%

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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### Understanding the Distribution of Widget Weights at The Acme Company The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 43 ounces and a standard deviation of 8 ounces. ### Using the Standard Deviation Rule (Empirical Rule) The Standard Deviation Rule, also known as the Empirical Rule, helps in understanding the distribution of data in a bell curve. The image below should assist in visualizing this rule: **Empirical Rule Diagram:** - The diagram illustrates a normal distribution curve with the mean (average) at the center (0). - The percentages indicate the proportion of data within certain standard deviations from the mean: - 34% of the data lies within one standard deviation below the mean (-1s) and one standard deviation above (1s). - 13.5% lies within one to two standard deviations below the mean (-2s) and one to two standard deviations above (2s). - 2.35% falls within two to three standard deviations below the mean (-3s) and two to three standard deviations above (3s). - 0.15% lies beyond three standard deviations below (-3s) and three standard deviations above (3s). ### Practice Questions To solidify your understanding, answer the following questions based on the information above: a) **95% of the widget weights lie between ____ and ____ ounces.** b) **What percentage of the widget weights lie between 35 and 59 ounces?** - ____ c) **What percentage of the widget weights lie above 19 ounces?** - ____ ### Analyzing the Questions - **Question (a):** Utilizes the approximate rule that 95% of data in a normal distribution falls within two standard deviations of the mean. - **Question (b):** Calculated by determining the area between the specified weights. - **Question (c):** Calculated by considering the area to the right of the given value on the distribution. Use the standard deviation (8 ounces) and mean (43 ounces) provided to calculate the answers accordingly and round your results to the nearest percentage where necessary.
Transcribed Image Text:### Understanding the Distribution of Widget Weights at The Acme Company The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 43 ounces and a standard deviation of 8 ounces. ### Using the Standard Deviation Rule (Empirical Rule) The Standard Deviation Rule, also known as the Empirical Rule, helps in understanding the distribution of data in a bell curve. The image below should assist in visualizing this rule: **Empirical Rule Diagram:** - The diagram illustrates a normal distribution curve with the mean (average) at the center (0). - The percentages indicate the proportion of data within certain standard deviations from the mean: - 34% of the data lies within one standard deviation below the mean (-1s) and one standard deviation above (1s). - 13.5% lies within one to two standard deviations below the mean (-2s) and one to two standard deviations above (2s). - 2.35% falls within two to three standard deviations below the mean (-3s) and two to three standard deviations above (3s). - 0.15% lies beyond three standard deviations below (-3s) and three standard deviations above (3s). ### Practice Questions To solidify your understanding, answer the following questions based on the information above: a) **95% of the widget weights lie between ____ and ____ ounces.** b) **What percentage of the widget weights lie between 35 and 59 ounces?** - ____ c) **What percentage of the widget weights lie above 19 ounces?** - ____ ### Analyzing the Questions - **Question (a):** Utilizes the approximate rule that 95% of data in a normal distribution falls within two standard deviations of the mean. - **Question (b):** Calculated by determining the area between the specified weights. - **Question (c):** Calculated by considering the area to the right of the given value on the distribution. Use the standard deviation (8 ounces) and mean (43 ounces) provided to calculate the answers accordingly and round your results to the nearest percentage where necessary.
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