The Basic Practice of Statistics 7th Edition

Published by W. H. Freeman
ISBN 10: 146414253X
ISBN 13: 978-1-46414-253-6

Chapter 15 - Sampling Distributions - Apply Your Knowledge - Page 355: 15.9a

Answer

0.7698

Work Step by Step

Here, we have n = 100, $μ = μ_{x̅} = 115$, σ = 25 $σ_{x̅} = \frac{σ}{\sqrt n} = \frac{25 }{\sqrt 100} = 2.5$ We need to calculate the z score for the probability that x̅ takes a value between 112 and 118 mg/dL. $z = \frac{x̅ - μ_{x̅}}{σ_{x̅}} = \frac{112-115}{2.5} = -1.2$ $z = \frac{x̅ - μ_{x̅}}{σ_{x̅}} = \frac{118-115}{2.5} = 1.2$ Using Table A of the book, we have: P(-1.2 < z < 1.2) = P(z < 1.2) - P(z > -1.2) = 0.8849 - 0.1151 = 0.7698
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