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: 32


a) Too high. b)5.5524 and 5.7876

Work Step by Step

a)$z=\frac{value-mean}{standard \ deviation}=\frac{5.7-5.67}{0.06}=0.5.$ $z=\frac{value-mean}{standard \ deviation}=\frac{5.64-5.67}{0.06}=-0.5.$ By using the table the corresponding probability: 0.6915-0.3085=0.3830=38.3%. Hence 100%-38.3%=61.7% is rejected, which is too high, it is more than half of the legal quarters. b)By using the table, the z-score corresponding to 0.025 and 0.975: z=$\pm 1.645$. Hence the corresponding values:$mean+z⋅standard \ deviation=5.67-1.96⋅0.06=5.5524.$ $mean+z⋅standard \ deviation=5.67+1.96⋅0.06=5.7876.$
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