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 - Basic Skills and Concepts - Page 270: 29


a) 91.77%. b)0.01% c)2.15, no.

Work Step by Step

a)$z=\frac{value-mean}{standard \ deviation}=\frac{2-1.184}{0.587}=1.39$. By using the table the corresponding probability: 0.9177=91.77%. b)$z=\frac{value-mean}{standard \ deviation}=\frac{4-1.184}{0.587}=4.8$. By using the table the corresponding probability: 1-0.9999=0.0001=0.01%. c)By using the table, the z-score corresponding to 1-0.05=0.95: z=1.645. Hence the corresponding value:$mean+z⋅standard \ deviation=1.184+1.645⋅0.587=2.15.$ Hence not all earthquakes above the 95th percentile will cause indoor items to shake, because it is less than 4.
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