Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321755936
ISBN 13: 978-0-32175-593-3

Chapter 4 - Discrete Random Variables - Exercises 4.50 - 4.76 - Applying the Concepts - Basic - Page 205: 4.62e

Answer

$p(x\geq3)=.945$

Work Step by Step

$q=1-p=1-.5=.5$ $p(x)=\begin{pmatrix} n \\ x \end{pmatrix}p^xq^{n-x}$ $p(x=0)=\begin{pmatrix} 10 \\ 0 \end{pmatrix}(.5)^0(.5)^{10-0}=\frac{10!}{0!(10-0)!}(.5)^{10}=\frac{10!}{10!}(.5)^{10}=(.5)^{10}$ $p(x=1)=\begin{pmatrix} 10 \\ 1 \end{pmatrix}(.5)^1(.5)^{10-1}=\frac{10!}{1!(10-1)!}(.5)^{10}=\frac{10(9!)}{9!(1!)}(.5)^{10}=10(.5)^{10}$ $p(x=2)=\begin{pmatrix} 10 \\ 2 \end{pmatrix}(.5)^2(.5)^{10-2}=\frac{10!}{2!(10-2)!}(.5)^{10}=\frac{10(9)(8!)}{2!(8!)}(.5)^{10}=45(.5)^{10}$ $p(x\geq3)=1-p(x\lt3)=1-p(x=0)-p(x=1)-p(x=2)=1-(.5)^{10}-10(.5)^{10}-45(.5)^{10}=1-56(.5)^{10}=.945$
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