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Biology The heights of men in a survey are distributed normally about the mean.Use the graph for Exercises 1 $-4 .$The mean of the data is $70,$ and the standard deviation is $2.5 .$ About what percent of men are within one standard deviation of the mean in height?

For a normally distributed data, 68$\%$ of data fall within one standard deviation of the mean.Therefore 68$\%$ of men fall within one standard deviation of mean height. Here the heights withinone standard deviation of mean is between 67.5 and 72.5

Precalculus

Geometry

Intro Stats / AP Statistics

Chapter 12

Probability And Statistics

Section 7

Normal Distributions

Introduction to Combinatorics and Probability

Probability

Graphs and Statistics

Descriptive Statistics

Probability Topics

University of Michigan - Ann Arbor

University of Nottingham

Boston College

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you're asked to find what percentage of men are between one standard deviation above and once they're deviation below the mean. So we know that our mean is equal to 70 are standard deviation is equal to 2.5 and we're going to use the formula. Z is equal to ah value minus the mean over standard deviation to find where ah one and negative one standard deviations would be from army. So to start will set one equal to Z because we want one center deviation above one is equal to you. Minus are mean of 70 over 2.5, and that gives us that you was equal to 72.5. So it's once they're deviation above our means. For once in your deviation below will set C equal to negative point, which gives us negative One is equal to B minus 70 over 2.5. Therefore, V is equal to 67.5, so 72.5 is above and 67.5 is one standard deviation below. So that means we're looking at the following heights. We want to look at heights from 68 inches from 2 72 inches to find where these men lay and what percentage they encompass. So our percent is equal to 11.5% from our graph for 68 inches, plus 13% for 69 inches, plus 16% for 70 inches. Waas, 14% for 71 inches, plus 12% for 72 inches and adding that up, we get 66.5% which is close to the 68% that is expected within one standard deviation above or below army.

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