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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 35 ounces and a standard deviation of 7 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule (see image below). Do not use normalcdf on your calculator.

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 35 ounces and a standard deviation of 7 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule (see image below). Do not use normalcdf on your calculator.

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
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**Title: Understanding Widget Weight Distribution using the Standard Deviation Rule** The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 35 ounces and a standard deviation of 7 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. **Questions:** a) 95% of the widget weights lie between _____ and _____. b) What percentage of the widget weights lie between 14 and 49 ounces? _____ % c) What percentage of the widget weights lie below 42? _____ % **Graph Explanation:** Below is a normal distribution graph indicating the mean and standard deviations: - The horizontal axis represents the widget weights. - The vertical axis represents the frequency of these weights. - The center of the distribution is marked by the mean (35 ounces). - From the center, each division represents a standard deviation (7 ounces). **Color-coded regions:** - The red region in the middle represents the mean and covers 68% of the data (34% on each side of the mean). - The pink regions, adjacent to the red region, each cover an additional 13.5%, making a combined total of 95% within two standard deviations of the mean. - The blue regions, adjacent to the pink regions, each cover 2.35%, extending to three standard deviations from the mean. - The green regions, at the tails of the distribution, each cover 0.15%, extending beyond three standard deviations from the mean. **Understanding the Graph:** - Within one standard deviation (mean ± 1 SD, i.e., 35 ± 7): 68% of the data - Within two standard deviations (mean ± 2 SD, i.e., 35 ± 14): 95% of the data - Within three standard deviations (mean ± 3 SD, i.e., 35 ± 21): 99.7% of the data Use this graph and the Standard Deviation Rule to fill out the blanks and calculate the required percentages for the questions listed above.
Transcribed Image Text:**Title: Understanding Widget Weight Distribution using the Standard Deviation Rule** The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 35 ounces and a standard deviation of 7 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. **Questions:** a) 95% of the widget weights lie between _____ and _____. b) What percentage of the widget weights lie between 14 and 49 ounces? _____ % c) What percentage of the widget weights lie below 42? _____ % **Graph Explanation:** Below is a normal distribution graph indicating the mean and standard deviations: - The horizontal axis represents the widget weights. - The vertical axis represents the frequency of these weights. - The center of the distribution is marked by the mean (35 ounces). - From the center, each division represents a standard deviation (7 ounces). **Color-coded regions:** - The red region in the middle represents the mean and covers 68% of the data (34% on each side of the mean). - The pink regions, adjacent to the red region, each cover an additional 13.5%, making a combined total of 95% within two standard deviations of the mean. - The blue regions, adjacent to the pink regions, each cover 2.35%, extending to three standard deviations from the mean. - The green regions, at the tails of the distribution, each cover 0.15%, extending beyond three standard deviations from the mean. **Understanding the Graph:** - Within one standard deviation (mean ± 1 SD, i.e., 35 ± 7): 68% of the data - Within two standard deviations (mean ± 2 SD, i.e., 35 ± 14): 95% of the data - Within three standard deviations (mean ± 3 SD, i.e., 35 ± 21): 99.7% of the data Use this graph and the Standard Deviation Rule to fill out the blanks and calculate the required percentages for the questions listed above.
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