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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 36 ounces and a standard deviation of 10 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 68% of the widget weights lie between and b) What percentage of the widget weights lie between 16 and 46 ounces? c) What percentage of the widget weights lie below 66 ?

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 36 ounces and a standard deviation of 10 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 68% of the widget weights lie between and b) What percentage of the widget weights lie between 16 and 46 ounces? c) What percentage of the widget weights lie below 66 ?

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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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 36 ounces and a standard deviation of 10 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 68% of the widget weights lie between and b) What percentage of the widget weights lie between 16 and 46 ounces? c) What percentage of the widget weights lie below 66 ? Ouortion Holn: Dlidon
Transcribed Image Text:The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 36 ounces and a standard deviation of 10 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 68% of the widget weights lie between and b) What percentage of the widget weights lie between 16 and 46 ounces? c) What percentage of the widget weights lie below 66 ? Ouortion Holn: Dlidon
Expert Solution
Step 1

a)

Empirical rule:

  • The probability of the observation lies within 1 standard deviation of the mean, under the normal curve, is about 0.68.
  • The probability of the observation lies within 2 standard deviations of the mean, under the normal curve, is about 0.95.
  • The probability of the observation lies within 3 standard deviations of the mean, under the normal curve, is about 0.997.
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