Statistics: Informed Decisions Using Data (4th Edition)

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

Chapter 6 - Section 6.2 - Assess Your Understanding - Vocabulary and Skill Building - Page 344: 31a

Answer

See the picture.

Work Step by Step

$P(x)={}_nC_{x}~p^x~(1-p)^{n-x}$ n = 9, p = 0.75 and 1 - p = 0.25 $P(0)={}_{9}C_{0}\times0.75^0\times0.25^9=\frac{9!}{0!\times9!}\times1\times0.25^9=1\times1\times0.25^9=0.000003815$ $P(1)={}_{9}C_{1}\times0.75^1\times0.25^8=\frac{9!}{1!\times8!}\times0.75^1\times0.25^8=9\times0.75\times0.25^8=0.0001030$ $P(2)={}_{9}C_{2}\times0.75^2\times0.25^7=\frac{9!}{2!\times7!}\times0.75^2\times0.25^7=36\times0.75^2\times0.25^7=0.001236$ $P(3)={}_{9}C_{3}\times0.75^3\times0.25^6=\frac{9!}{3!\times6!}\times0.75^3\times0.25^6=84\times0.75^3\times0.25^6=0.008652$ $P(4)={}_{9}C_{4}\times0.75^4\times0.25^5=\frac{9!}{4!\times5!}\times0.75^4\times0.25^5=126\times0.75^4\times0.25^5=0.03893$ $P(5)={}_{9}C_{5}\times0.75^5\times0.25^4=\frac{9!}{5!\times4!}\times0.75^5\times0.25^4=126\times0.2^5\times0.8^5=0.1168$ $P(6)={}_{9}C_{6}\times0.75^6\times0.25^3=\frac{9!}{6!\times3!}\times0.75^6\times0.25^3=84\times0.75^6\times0.25^3=0.2336$ $P(7)={}_{9}C_{7}\times0.75^7\times0.25^2=\frac{9!}{7!\times2!}\times0.75^7\times0.25^2=36\times0.75^7\times0.25^2=0.3003$ $P(8)={}_{9}C_{8}\times0.75^8\times0.25^1=\frac{9!}{8!\times1!}\times0.75^8\times0.25=9\times0.75^8\times0.25=0.2253$ $P(9)={}_{9}C_{9}\times0.75^9\times0.25^0=\frac{9!}{9!\times0!}\times0.75^9\times1=1\times0.75^9\times1=0.07508$
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