The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 38 ounces and a standard deviation of 10 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) 99.7% of the widget weights lie between and b) What percentage of the widget weights lie between 18 and 68 ounces? c) What percentage of the widget weights lie above 28 ?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
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Chapter1: Starting With Matlab
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**The Acme Company manufactures widgets.** 

The distribution of widget weights is bell-shaped. The widget weights have a mean of 38 ounces and a standard deviation of 10 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) **99.7% of the widget weights lie between** [______] **and** [______].

b) **What percentage of the widget weights lie between 18 and 68 ounces?** [______]%

c) **What percentage of the widget weights lie above 28?** [______]%

---

**Explanation of Diagram:**

The diagram at the bottom of the image is a bell curve (normal distribution) illustrating the Empirical Rule:

- The central line is labeled as "x-bar" (mean), at 38 ounces.
- The shaded areas represent the distribution of data around the mean:
  - 34% of data lies within one standard deviation (10 ounces) to the left or right of the mean.
  - 13.5% lies between one and two standard deviations from the mean.
  - 2.35% lies between two and three standard deviations from the mean.
  - 0.15% lies beyond three standard deviations on either side.
Transcribed Image Text:**The Acme Company manufactures widgets.** The distribution of widget weights is bell-shaped. The widget weights have a mean of 38 ounces and a standard deviation of 10 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) **99.7% of the widget weights lie between** [______] **and** [______]. b) **What percentage of the widget weights lie between 18 and 68 ounces?** [______]% c) **What percentage of the widget weights lie above 28?** [______]% --- **Explanation of Diagram:** The diagram at the bottom of the image is a bell curve (normal distribution) illustrating the Empirical Rule: - The central line is labeled as "x-bar" (mean), at 38 ounces. - The shaded areas represent the distribution of data around the mean: - 34% of data lies within one standard deviation (10 ounces) to the left or right of the mean. - 13.5% lies between one and two standard deviations from the mean. - 2.35% lies between two and three standard deviations from the mean. - 0.15% lies beyond three standard deviations on either side.
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