Statistics: Informed Decisions Using Data (4th Edition)

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

Chapter 6 - Review - Review Exercises - Page 356: 8a

Answer

See the picture.

Work Step by Step

$P(x)={}_nC_{x}~p^x~(1-p)^{n-x}$ n = 8, p = 0.75 and 1 - p = 0.25 $P(0)={}_8C_{0}\times0.75^0\times0.25^{8}=\frac{8!}{0!\times8!}\times1\times0.25^8=0.0000153$ $P(1)={}_8C_{1}\times0.75^1\times0.25^7=\frac{8!}{1!\times7!}\times0.75\times0.25^7=0.000366$ $P(2)={}_8C_{2}\times0.75^2\times0.25^5=\frac{8!}{2!\times6!}\times0.75^2\times0.25^6=0.00385$ $P(3)={}_8C_{3}\times0.75^3\times0.25^5=\frac{8!}{3!\times5!}\times0.75^3\times0.25^5=0.0231$ $P(4)={}_8C_{4}\times0.75^4\times0.25^4=\frac{8!}{4!\times4!}\times0.75^4\times0.25^4=0.0865$ $P(5)={}_8C_{5}\times0.75^5\times0.25^3=\frac{8!}{5!\times3!}\times0.75^5\times0.25^3=0.2076$ $P(6)={}_8C_{6}\times0.75^6\times0.25^2=\frac{8!}{6!\times2!}\times0.75^6\times0.25^2=0.3115$ $P(7)={}_8C_{7}\times0.75^7\times0.25^1=\frac{8!}{7!\times1!}\times0.75^7\times0.25=0.2670$ $P(8)={}_8C_{8}\times0.75^8\times0.25^0=\frac{8!}{8!\times0!}\times0.75^8\times1=0.1001$
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