Elementary Statistics (12th Edition)

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

Chapter 5 - Discrete Probability Distributions - 5-3 Binomial Probability Distributions - Basic Skills and Concepts: 38

Answer

0.6324, it is not a good idea to book 21 passengers.

Work Step by Step

The bad case is if more than 19 passengers turn up. We need to find the probability of this and subtract it from 1 to get the probability of not being too many people. $P(X\leq19)=1-(P(X=20)+P(X=21))=1-{21 \choose 20} \cdot 0.9005^{20} \cdot 0.0995^1-{21 \choose 21} \cdot 0.9005^{21} \cdot 0.0995^0=1-0.2569-0.1107=0.6324. $ This is a quite low probability, the porbability of too many passengers is quite high, therefore it is not a good idea to book 21 passengers.
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