Elementary Statistics (12th Edition)

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

Chapter 5 - Discrete Probability Distributions - 5-5 Poisson Probability Distributions - Beyond the Basics: 17

Answer

a) We cannot use the Poisson distribution. b)The result gained by the Poisson distribution is not OK.

Work Step by Step

a) n=12, p=$\frac{1}{6}$, therefore $n\geq100$ is not satisfied, therefore we cannot use the Poisson distribution. b) Counting by the Poisson distribution: $\frac{2^3\cdot e^{-2}}{3!}=0.18$, whilst counting by the binomial distrbution:${12\choose 3}\cdot (\frac{1}{6})^3 \cdot (\frac{5}{6})^9=0.197.$ These two results are far from each other, so the result gained by the Poisson distribution is not OK.
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