MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Concept explainers

Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…
Mean, Median, Mode
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Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…
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**Normal Distribution of College Women's Heights** Assuming that the heights of college women are normally distributed with a mean (μ) of 63 inches and a standard deviation (σ) of 1.7 inches, answer the following questions. (Hint: Use the figure below with mean μ and standard deviation σ.) **Diagram Explanation:** The diagram is a bell-shaped curve representing the normal distribution, centered around the mean, μ (63 inches). The x-axis is labeled with values μ, μ ± σ, μ ± 2σ, and μ ± 3σ, denoting standard deviations from the mean. The areas under the curve are labeled to show percentages: - **2.35%** beyond μ ± 3σ - **13.5%** between μ ± 2σ and μ ± 3σ - **34%** between μ ± σ and μ ± 2σ - The area between μ - σ and μ + σ is the largest, covering **68%** of the data. - Cumulative percentages span **68%, 95%, and 99.7%** for 1, 2, and 3 standard deviations from the mean, respectively. **Questions:** (a) What percentage of women are taller than 63 inches? ___% (b) What percentage of women are shorter than 63 inches? ___% (c) What percentage of women are between 61.3 inches and 64.7 inches? ___% (d) What percentage of women are between 59.6 inches and 66.4 inches? ___%
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Transcribed Image Text:**Normal Distribution of College Women's Heights** Assuming that the heights of college women are normally distributed with a mean (μ) of 63 inches and a standard deviation (σ) of 1.7 inches, answer the following questions. (Hint: Use the figure below with mean μ and standard deviation σ.) **Diagram Explanation:** The diagram is a bell-shaped curve representing the normal distribution, centered around the mean, μ (63 inches). The x-axis is labeled with values μ, μ ± σ, μ ± 2σ, and μ ± 3σ, denoting standard deviations from the mean. The areas under the curve are labeled to show percentages: - **2.35%** beyond μ ± 3σ - **13.5%** between μ ± 2σ and μ ± 3σ - **34%** between μ ± σ and μ ± 2σ - The area between μ - σ and μ + σ is the largest, covering **68%** of the data. - Cumulative percentages span **68%, 95%, and 99.7%** for 1, 2, and 3 standard deviations from the mean, respectively. **Questions:** (a) What percentage of women are taller than 63 inches? ___% (b) What percentage of women are shorter than 63 inches? ___% (c) What percentage of women are between 61.3 inches and 64.7 inches? ___% (d) What percentage of women are between 59.6 inches and 66.4 inches? ___%
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