Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 6 - Normal Probability Distributions - 6-3 Applications of Normal Distributions - Beyond the Basics: 36

Answer

a)92.87% b)95.2% c)Yes.

Work Step by Step

a)$z=\frac{value-mean}{standard \ deviation}=\frac{20-24}{2.6}=-1.54.$ $z=\frac{value-mean}{standard \ deviation}=\frac{30-24}{2.6}=2.31.$ By using the table the corresponding probability: 0.9896-0.0618=0.9287=92.87%. b)$z=\frac{value-mean}{standard \ deviation}=\frac{19.5-24}{2.6}=-1.73.$ $z=\frac{value-mean}{standard \ deviation}=\frac{30.5-24}{2.6}=2.5.$ By using the table the corresponding probability: 0.9938-0.0418=0.952=95.2%. c) Yes it does because the difference between the result of a) and b) is more than 2%.
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