Elementary Statistics (12th Edition)

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

Chapter 6 - Normal Probability Distributions - 6-5 The Central Limit Theorem - Basic Skills and Concepts - Page 294: 17

Answer

a) $0.6517$ b) $0.9115$ c) Should be reduced.

Work Step by Step

a) We use the z-score to find: $z=\frac{167−182.9}{40.8}=−0.39$ Hence, using the table of z-scores, we find that this corresponds to a probability of $1−0.3483=0.6517$ b) We use the z-score to find: $z=\frac{167−182.9}{40.8/\sqrt{12}}=−1.35$ Thus, using the table of z-scores, we find that this corresponds to a probability of $1−0.0885=0.9115$ c) For safety standards, the probability is too low, hence the weight limit should be reduced.
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