Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 12 - Section 12.1 - Assess Your Understanding - Applying the Concepts - Page 598: 29c

Answer

$P(0)=0.3936$ $P(1)=0.3670$ $P(2)=0.1711$ $P(3)=0.0532$ $P(4~or~more~hits)=0.0151$

Work Step by Step

$P(x)=\frac{μ^x}{x!}e^{-μ}$ $μ=0.9323$ $P(0)=\frac{0.9323^0}{0!}e^{-0.9323}=0.3936$ $P(1)=\frac{0.9323^1}{1!}e^{-0.9323}=0.3670$ $P(2)=\frac{0.9323^2}{2!}e^{-0.9323}=0.1711$ $P(3)=\frac{0.9323^3}{3!}e^{-0.9323}=0.0532$ The event "4 or more hits" is the complement of the event "0 hits or 1 hit or 2 hits or 3 hits" Using the Complement Rule (see page 275): $P(4~or~more~hits)=P(X\geq4)=1-[P(0)+P(1)+P(2)+P(3)]=1-(0.3936+0.3670+0.1711+0.0532)=0.0151$
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