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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 48 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. a) 68% of the widget weights lie between ? and ? b) What percentage of the widget weights lie between 27 and 55 ounces?                 % c) What percentage of the widget weights lie below 62 ?        %

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 48 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. a) 68% of the widget weights lie between ? and ? b) What percentage of the widget weights lie between 27 and 55 ounces?                 % c) What percentage of the widget weights lie below 62 ?        %

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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 48 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.

a) 68% of the widget weights lie between ? and ?

b) What percentage of the widget weights lie between 27 and 55 ounces?                 %

c) What percentage of the widget weights lie below 62 ?        %

### Understanding the Normal Distribution The image illustrates a normal distribution, a fundamental concept in statistics. This bell-shaped curve is symmetrical around the mean, representing how data points are distributed across a dataset. The mean is located at the center of the curve, marked as 0. #### Key Features of the Normal Distribution: 1. **Standard Deviations (σ):** - The curve is divided into sections by standard deviations from the mean, denoted as -3σ to +3σ. - One standard deviation from the mean (1σ) covers approximately 68% of the data (34% on each side). - Two standard deviations (2σ) cover about 95% of the data (additional 13.5% on each side beyond 1σ). - Three standard deviations (3σ) encompass about 99.7% of the data (adding 2.35% on each side beyond 2σ). 2. **Percentages Under the Curve:** - **Center (Red Area):** 34% of the data lies between the mean (0σ) and +1σ and another 34% from the mean to -1σ. - **Middle Sections (Blue Area):** From +1σ to +2σ and -1σ to -2σ, 13.5% of the data falls within each section. - **Outer Sections (Green Area):** Beyond ±2σ, 2.35% falls in each section up to ±3σ. - **Extremes:** Only 0.15% of data falls below -3σ and above +3σ. This distribution is crucial for predicting outcomes and probabilities in various fields, including psychology, finance, and natural sciences. Understanding these segments helps in identifying the likelihood of data points falling within a certain range.
Transcribed Image Text:### Understanding the Normal Distribution The image illustrates a normal distribution, a fundamental concept in statistics. This bell-shaped curve is symmetrical around the mean, representing how data points are distributed across a dataset. The mean is located at the center of the curve, marked as 0. #### Key Features of the Normal Distribution: 1. **Standard Deviations (σ):** - The curve is divided into sections by standard deviations from the mean, denoted as -3σ to +3σ. - One standard deviation from the mean (1σ) covers approximately 68% of the data (34% on each side). - Two standard deviations (2σ) cover about 95% of the data (additional 13.5% on each side beyond 1σ). - Three standard deviations (3σ) encompass about 99.7% of the data (adding 2.35% on each side beyond 2σ). 2. **Percentages Under the Curve:** - **Center (Red Area):** 34% of the data lies between the mean (0σ) and +1σ and another 34% from the mean to -1σ. - **Middle Sections (Blue Area):** From +1σ to +2σ and -1σ to -2σ, 13.5% of the data falls within each section. - **Outer Sections (Green Area):** Beyond ±2σ, 2.35% falls in each section up to ±3σ. - **Extremes:** Only 0.15% of data falls below -3σ and above +3σ. This distribution is crucial for predicting outcomes and probabilities in various fields, including psychology, finance, and natural sciences. Understanding these segments helps in identifying the likelihood of data points falling within a certain range.
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