Elementary Statistics (12th Edition)

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

Chapter 5 - Discrete Probability Distributions - 5-4 Parameters for Binomial Distributions - Basic Skills and Concepts: 14

Answer

a) Mean:140. Standard deviation:8.37. b)It is unusually low. The touch therapist doesn't seem to have any special ability.

Work Step by Step

In this case the probability of guessing well is 0.5. a) Mean=$n\cdot p=280 \cdot 0.5=140$. Standard deviation: $\sqrt{n \cdot p \cdot (1-p)}=\sqrt{280 \cdot 0.5 \cdot 0.5}=8.37.$ b) If a value is unusual, then it is more than two standard deviations far from the mean. $Minimum \ usual \ value=mean-2\cdot(standard \ deviation)=140-2\cdot8.37=123.26$ $Maximum \ usual \ value=mean+2\cdot(standard \ deviation)=140+2\cdot8.37=156.74$. 123 is less than the lower bound, therefore it is an unusually low value. The touch therapist's 'ability' made things worse than randomly guessing the hand, therefore the touch therapist doesn't seem to have any special ability.
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.