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Math Statistics Essential Statistics (2nd Edition)

(a) To find: The percentage of SAT takers that have scored between 450 and 500. The percentage is 19.35% Given information: Mean μ = 495 Standard deviation σ = 100 Formula used: The formula to compute the z-score is: z = x − μ σ Where, x is the raw score μ is the population mean. σ is the population standard deviation. Calculation: Consider, X be the random variable that shows the scores scored by SAT takers is distributed normally. The percentage is calculated as: P 450 < X < 500 = P 450 − μ σ < x − μ σ < 500 − μ σ = P 450 − 495 100 < x − μ σ < 500 − 495 100 = P − 0.45 < Z < 0.05 = P Z < 0.05 − P Z < − 0.45 = 0.1935 The required percentage is 19.35%. (b) To find: The percentage of SAT takers that have scored between 500 and 600. The percentage is 33.32% The percentage is calculated as: P 500 < X < 600 = P 5000 − μ σ < x − μ σ < 600 − μ σ = P 500 − 495 100 < x − μ σ < 600 − 495 100 = P 0.05 < Z < 1.05 = P Z < 1.05 − P Z < 0.05 = 0.3332 The required percentage is 33.32%.

(a) To find: The percentage of SAT takers that have scored between 450 and 500. The percentage is 19.35% Given information: Mean μ = 495 Standard deviation σ = 100 Formula used: The formula to compute the z-score is: z = x − μ σ Where, x is the raw score μ is the population mean. σ is the population standard deviation. Calculation: Consider, X be the random variable that shows the scores scored by SAT takers is distributed normally. The percentage is calculated as: P 450 < X < 500 = P 450 − μ σ < x − μ σ < 500 − μ σ = P 450 − 495 100 < x − μ σ < 500 − 495 100 = P − 0.45 < Z < 0.05 = P Z < 0.05 − P Z < − 0.45 = 0.1935 The required percentage is 19.35%. (b) To find: The percentage of SAT takers that have scored between 500 and 600. The percentage is 33.32% The percentage is calculated as: P 500 < X < 600 = P 5000 − μ σ < x − μ σ < 600 − μ σ = P 500 − 495 100 < x − μ σ < 600 − 495 100 = P 0.05 < Z < 1.05 = P Z < 1.05 − P Z < 0.05 = 0.3332 The required percentage is 33.32%.

Essential Statistics (2nd Edition)

Essential Statistics (2nd Edition)

2nd Edition

ISBN: 9780134134406

Author: Robert Gould, Colleen N. Ryan, Rebecca Wong

Publisher: PEARSON

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Chapter 6, Problem 34SE

Chapter 6, Problem 36SE

Chapter 6 Solutions

Essential Statistics (2nd Edition)

Ch. 6 - Prob. 35SE

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