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The heights of men at a gym are normally distributed with a mean of 70 inches and a standard deviation of 5 inches. What percent of men are, a) Between 60 inches and 75 inches? b) Greater than 72 inches? c) Less than 60 inches?

The heights of men at a gym are normally distributed with a mean of 70 inches and a standard deviation of 5 inches. What percent of men are, a) Between 60 inches and 75 inches? b) Greater than 72 inches? c) Less than 60 inches?

MATLAB: An Introduction with Applications
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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**Title: Understanding Normal Distribution of Heights in a Gym Setting** **Introduction:** In this example, we're examining the heights of men at a gym, which are normally distributed. **Given Data:** - **Mean Height:** 70 inches - **Standard Deviation:** 5 inches **Questions:** a) What percent of men have heights between 60 inches and 75 inches? b) What percent of men have heights greater than 72 inches? c) What percent of men have heights less than 60 inches? **Explanation of Normal Distribution:** A normal distribution is a probability distribution that is symmetric about the mean. In this scenario, it means most men have heights around the average (mean) of 70 inches. The bell curve represents this distribution, where the highest point is at the mean, and the spread is determined by the standard deviation. **Key Concepts:** - **Mean (70 inches):** Central point of data. - **Standard Deviation (5 inches):** Measure of the spread of heights around the mean. Understanding and applying these concepts allows us to calculate the probabilities for the specified ranges.
Transcribed Image Text:**Title: Understanding Normal Distribution of Heights in a Gym Setting** **Introduction:** In this example, we're examining the heights of men at a gym, which are normally distributed. **Given Data:** - **Mean Height:** 70 inches - **Standard Deviation:** 5 inches **Questions:** a) What percent of men have heights between 60 inches and 75 inches? b) What percent of men have heights greater than 72 inches? c) What percent of men have heights less than 60 inches? **Explanation of Normal Distribution:** A normal distribution is a probability distribution that is symmetric about the mean. In this scenario, it means most men have heights around the average (mean) of 70 inches. The bell curve represents this distribution, where the highest point is at the mean, and the spread is determined by the standard deviation. **Key Concepts:** - **Mean (70 inches):** Central point of data. - **Standard Deviation (5 inches):** Measure of the spread of heights around the mean. Understanding and applying these concepts allows us to calculate the probabilities for the specified ranges.
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The given mean is 70 and standard deviation is 5.

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