The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 49 ounces and a standard deviation of 6 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 95% of the widget weights lie between oz and OZ b) What percentage of the widget weights lie between 31 and 61 ounces? % c) What percentage of the widget weights lie above 43 ?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
**The Acme Company manufactures widgets.** The distribution of widget weights is bell-shaped. The widget weights have a mean of 49 ounces and a standard deviation of 6 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

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

a) 95% of the widget weights lie between ___ oz and ___ oz

b) What percentage of the widget weights lie between 31 and 61 ounces? ___ %

c) What percentage of the widget weights lie above 43? ___ %

**Explanation:**

The Empirical Rule states that for a bell-shaped distribution:

- Approximately 68% of data falls within 1 standard deviation from the mean.
- Approximately 95% falls within 2 standard deviations.
- Approximately 99.7% falls within 3 standard deviations.

For question (a), calculate the range using 2 standard deviations (49 ± 2*6).

For question (b), determine the percentage that falls between 31 and 61 ounces, considering that this range likely encompasses all standard deviations.

For question (c), calculate the percentage above a specified value by finding the z-score or referring to symmetry around the mean if applicable.

Sketching a normal distribution curve could assist in visualizing these probabilities.
Transcribed Image Text:**The Acme Company manufactures widgets.** The distribution of widget weights is bell-shaped. The widget weights have a mean of 49 ounces and a standard deviation of 6 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. **Suggestion:** Sketch the distribution in order to answer these questions. a) 95% of the widget weights lie between ___ oz and ___ oz b) What percentage of the widget weights lie between 31 and 61 ounces? ___ % c) What percentage of the widget weights lie above 43? ___ % **Explanation:** The Empirical Rule states that for a bell-shaped distribution: - Approximately 68% of data falls within 1 standard deviation from the mean. - Approximately 95% falls within 2 standard deviations. - Approximately 99.7% falls within 3 standard deviations. For question (a), calculate the range using 2 standard deviations (49 ± 2*6). For question (b), determine the percentage that falls between 31 and 61 ounces, considering that this range likely encompasses all standard deviations. For question (c), calculate the percentage above a specified value by finding the z-score or referring to symmetry around the mean if applicable. Sketching a normal distribution curve could assist in visualizing these probabilities.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman