Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 11 Data Analysis and Statistics - Extension - Approximate Binomial Distributions and Test Hypotheses - Practice - Page 765: 19


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Work Step by Step

85% are generally happy, hence $p=0.85$ There are 26 people, $n=26$ Mean: $\bar x=np\\=26\times 0.85\\=22.1$ Standard deviation: $\sigma =\sqrt np(1-p)\\=\sqrt 26\times0.85\times(1-0.85)\\=1.82$ We can find the z-score by applying the formula: $z=\frac{x-\bar x}{\sigma}=\frac{19-22.1}{1.81}\approx-1.7$ We will use the table to find $P(x \leq 19)\approx P(z\leq-1.7)\approx0.0446$ Hence, we reject the survey’s findings.
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