Explanation Given: The large scale of aggressive and passive personalities of a people was measured in a test devised where the scores are distributed normally. If the measurement of the people scores higher than 10% then it will consider as the aggressive, next 20% as moderately aggressive, 40% as average, next 20% as moderately passive and lowest 10% as the passive, respectively. Calculation: The average score of the aggressive and passive personality people with the mean is μ = 50 and standard deviation as σ = 10 . Consider the highest aggressive and passive scores x 1 = 10 % x 2 = 20 % x 3 = 20 % x 4 = 10 % as the corresponding z 1 , z 2 , z 3 and z 4 scores. Solve x 1 , x 2 , x 3 , x 4 for the z 1 , z 2 , z 3 and z 4 . From Figure 1, it is observed that the area between μ and x 3 is 20% that is 0.2. Use the table of area under normal curve, the z score corresponding to the area of 0.2 is 0.52. Substitute the value of z = 0.52 , μ = 50 and σ = 10 in the general formula of the standard deviation is given by z = x − μ σ , where σ is the standard deviation. Compute x 3 by substituting z = 0.52 , μ = 50 and σ = 10 in the general formula of the standard deviation is given by z = x − μ σ as follows, 0.52 = x 3 − 50 10 x 3 − 50 = 5.2 x 3 = 55.2 Therefore, the value of x 3 is 55.2. Compute x 2 by substituting z = − 0.52 , μ = 50 and σ = 10 in the general formula of the standard deviation is given by z = x − μ σ

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter 11.4, Problem 86E

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To find: The ranges of the score that will covered by five designations.

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Chapter 11.4, Problem 85E

Chapter 11, Problem 1RE

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Chapter 11 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The ranges of the score that will covered by five designations.

Solution Summary: The author explains the ranges of the score that will cover by five designations: the people having passive personality's measures a percentage of 37.2 or less.

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To find: The ranges of the score that will covered by five designations.

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Chapter 11 Solutions