PH 167_J_Nguyen_HW 4_Spring 2024

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University of the Pacific, Stockton *

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Statistics

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Apr 3, 2024

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HW 4 Chapter 7: Exercises 7.2, 7.5, 7.6 a and b, 7.7 Chapter 8: Review Questions: 8.14 and 8.15; Exercises: 8.12 7.2 N( 138, 7) Heights of 10 year old boys (cm) Middle 95% is contained in + / - 2 standard deviations Lower Value of Range 124 1/2-pt Upper Value of Range 152 The Tallest 2.5% are 151.72 cm or taller 1/2-pt 7.5 N( 138, 7) Heights of 10 year old boys (cm) (3-pts) a.) Proportion less than 150 cm Z-value 1.71 ==> Table B Equivalent 0.9564 Pr(X < 150) = 95.64% 1-pt b.) Proportion less than 140 cm Pr(X < 140) Z-value 0.28 ==> Table B Equivalent 0.6103 Pr(X < 140) = 61.03% 1-pt c.) The Proportion betrween 150 cm and 140 cm Pr(140 <= X <= 150) Pr(140 <= X <= 150) 34.61 1-pt 7.6 N (176.9, 7.1) Heights of 20 year old men (cm) a.) Proprtion at least 183 cm tall Pr(X >= 183) This is the Compliment of Pr( X < 183) Find Pr( X < 183) Z-value 0.85 ==> Table B Equivalent 0.8023 Pr(X >= 183) = 1 - Pr(X < 183) 19.77% 1/2-pt
7.6 Continued b.) N (163.3, 6.5) Heights of 20 year old women (cm) Proportion at least 183 cm tall Pr(X > 183) This is the Compliment of Pr( X < 183) Find Pr( X < 183) Z-value 3.03 ==> Table B Equivalent 0.9987 Pr(X > 183) = 1 - Pr(X < 183) 0.0013 1/2-pt 7.7 Modified - This problem has been modified from the text book What Heights for Men and for Women represents the 90th percentile? The Z-value representing the 90th percentile is 1.34 186.1 cm 171.7 cm Review Questions: 8.14, 8.15 8.14 What is the name of the statistical principle that states Central limit theorem 8.15 What is another term for the Standard Deviation of the Sample Mean? Standard error of the mean Exercise 8.12 8.12 The characteristics of the Distribution of Sample Means a.) the shape will be: symmetrical and bell shaped b.) it will be centered at the: population mean (μ) c.) with a standard deviation of: (insert the d.) the Theorem is called the central limit theorem For Men: Height X is: X = + (Z x σ) For Women: Height X is: X = + (Z x σ ) "The value of will approach µ as n gets larger and larger"? 𝝈 /√ 𝒏
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