?? **Text Description:**The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 58 ounces and a standard deviation of 10 ounces. Use the Empirical Rule.Suggestion: Sketch the distribution in order to answer these questions.a) 99.7% of the widget weights lie between [text box: 28] and [text box: 88] ounces.b) What percentage of the widget weights lie between 48 and 88 ounces? [text box]c) What percentage of the widget weights lie below 78 ounces? [text box]**Additional Elements:**- There is an option labeled "Question Help: Video" for additional assistance.- A button labeled "Submit Question" is available for submission of the answers.**Diagram Explanation:**There are no specific graphs or diagrams included in the image. However, the suggestion indicates that a sketch of the bell-shaped distribution may assist in understanding and answering the questions using the Empirical Rule. The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical concept that helps in understanding the distribution of data in a normal distribution:- Approximately 68% of the data falls within one standard deviation of the mean.- Approximately 95% falls within two standard deviations.- Approximately 99.7% falls within three standard deviations.

Answered: The Acme Company manufactures widgets.…

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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**Text Description:**

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 58 ounces and a standard deviation of 10 ounces.

Use the Empirical Rule.

Suggestion: Sketch the distribution in order to answer these questions.

a) 99.7% of the widget weights lie between [text box: 28] and [text box: 88] ounces.

b) What percentage of the widget weights lie between 48 and 88 ounces? [text box]

c) What percentage of the widget weights lie below 78 ounces? [text box]

**Additional Elements:**

- There is an option labeled "Question Help: Video" for additional assistance.
- A button labeled "Submit Question" is available for submission of the answers.

**Diagram Explanation:**

There are no specific graphs or diagrams included in the image. However, the suggestion indicates that a sketch of the bell-shaped distribution may assist in understanding and answering the questions using the Empirical Rule. The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical concept that helps in understanding the distribution of data in a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% falls within two standard deviations.
- Approximately 99.7% falls within three standard deviations.

Expert Solution

Step 1: Introducing the given information

Let X is defined as the widget weights. The widget weights have a mean of 58 ounces and a standard deviation of 10 ounces.

The one standard deviation limits are,

$table row cell mu plus-or-minus sigma end cell equals cell open parentheses 58 minus 10 comma 58 plus 10 close parentheses end cell row blank equals cell open parentheses 48 comma 68 close parentheses end cell end table$

The two standard deviation limits are,

$table row cell mu plus-or-minus 2 sigma end cell equals cell 58 plus-or-minus open parentheses 2 cross times 10 close parentheses end cell row blank equals cell 58 plus-or-minus 20 end cell row blank equals cell open parentheses 58 minus 20 comma 58 plus 20 close parentheses end cell row blank equals cell open parentheses 38 comma 78 close parentheses end cell end table$

The three standard deviation limits are,

$table row cell mu plus-or-minus 3 sigma end cell equals cell 58 plus-or-minus open parentheses 3 cross times 10 close parentheses end cell row blank equals cell 58 plus-or-minus 30 end cell row blank equals cell open parentheses 58 minus 30 comma 58 plus 30 close parentheses end cell row blank equals cell open parentheses 28 comma 88 close parentheses end cell end table$

The distribution is,