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Chapter Sequences; Induction; The Binomial Theorem, Question P
College Algebra 10 by Michael Sullivan
College Algebra 10 Edition
Author:
Michael Sullivan
Edition:
10
ISBN:
9780321979476
Publisher:
PEARSON
Subject:
Algebra 2
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Chapter Sequences; Induction; The Binomial Theorem, Question Problem 20AYU

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The probability that a tune-up will take more than 2 hours and the probability that a tune-up will take less than 66 minutes. The probability that a tune-up will take more than 2 hours or 120 minutes is 0.16 and the probability that a tune-up will take less than 66 minutes is 0.025. Given: The distribution of time taken for a tune-up follows a normal distribution with mean μ = 102 and standard deviation σ = 18 . Concept used: The Empirical rule states that within one standard deviation of the mean, there is about 68% of the data, within two standard deviations of the mean, there is about 95% of the data, and within three standard deviations of the mean, there is about 99.7% of the data. Calculation: With reference to the normal distribution curve and empirical rule as shown above the one standard deviation and two standard deviations away from points are calculated as shown below μ − σ = 102 − 18 = 84 μ + σ = 102 + 18 = 120 μ − 2 σ = 102 − 2 × 18 = 66 μ + 2 σ = 102 + 2 × 18 = 138 Thus according to the empirical rule, 120 minutes is one standard deviation more than the mean, and the probability greater than the mean 102 is about 50% and the probability between the mean and 120 minutes is about 34%. Thus the probability that it takes more than 120 minutes for a tune-up is calculated as shown below P ( X > 120 ) = P ( X > 102 ) − P ( 102 < X < 120 ) P ( X > 120 ) = 0.5 − 0.34 P ( X > 120 ) = 0.16 . The probability that it takes more than 120 minutes for a tune-up is 0.16. Thus according to the empirical rule, 66 minutes is two standard deviations less than the mean, and the probability less than the mean 102 is about 50% and the probability between the mean and 66 minutes is about 34 % + 13.5 % = 47.5 % . Thus the probability that it takes less than 66 minutes for a tune-up is calculated as shown below P ( X < 66 ) = P ( X < 102 ) − P ( 66 < X < 102 ) P ( X < 66 ) = 0.5 − 0.475 P ( X < 66 ) = 0.025 The probability that it takes less than 66 minutes for a tune-up is 0.025. Conclusion: With reference to the empirical rule, the probability that a tune-up takes more than 120 minutes is 0.16 and the probability that a tune-up takes less than 66 minutes is 0.025.
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Question Text
Chapter Sequences; Induction; The Binomial Theorem, Question Problem 20AYU
TopicAll Topics
SubjectAlgebra 2
ClassClass 12
Answer TypeText solution:1