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 296: 22


0.9887, yes.

Work Step by Step

By using the Central Limit Theorem, the sample mean has a mean of $\mu$ and standard deviation of $\frac{\sigma}{\sqrt n}$. $z=\frac{value-mean}{standard \ deviation}=\frac{167.6-182.9}{\frac{40.8}{\sqrt{16}}}=-2.28.$ Using the table, the probability of z being more than -2.28 is equal to 1 minus the probability of z being less than -2.28, which is: 1-0.0113=0.9887. Therefore the pilot should take over the aeroplane because the probability of it being overloaded is very high.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.