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: 12

Answer

0.1922

Work Step by Step

By using the Central Limit Theorem, the sample mean has a mean of $\mu$ and standard deviation of $\frac{\sigma}{\sqrt n}$. $z=\frac{value-mean}{standard \ deviation}=\frac{182.9-174}{\frac{0.87}{\sqrt{16}}}=1.22.$ Using the table, the probability of z being more than 0.87 is equal to 1 minus the probability of z being less than 0.87, which is: 1-0.8078=0.1922. Therefore the elevator seems to be safe, because the probability of it being overloaded is not too close to 0. By using the outdated mean, the elevator will be safer because this increases it's probability of being overloaded and hence less people will be allowed into it.
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