document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=666404>Question 666404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Of those mountain climbers who attempt Mt. McKinley, only 65% reach the summit. In a random sample of 12 mountain climbers who are going to attempt Mt. McKinley, what is the probability of each of the following?<BR>\n" );
document.write( "a.)At least 8 reach the summit<BR>\n" );
document.write( "b.)no more than 8 reach the summit<BR>\n" );
document.write( "c.)6 to 10 reach the summit, including 6 and 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #414441 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=414441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You either reach the summit or you don't. Thus we have a binomial distribution.\r<BR>\n" );
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document.write( "a) P[x>=8] = P[x=8]+P[x=9]+P[x=10]+P[x=11]+P[x=12] = (12 choose 8) * (.65)^8 * (.35)^4 + (12 choose 9) * (.65)^9 * (.35)^3 + (12 choose 10) * (.65)^10 * (.35)^2 + (12 choose 11) * (.65)^11 * (.35)^1 + (12 choose 12) * (.65)^12 * (.35)^0 = .5833\r<BR>\n" );
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document.write( "b) P[x<=8] = P[x<8] + P[x=8] = (1-P[x>=8]) + P[x=8]. As you see, we used the complement. We already know what P[x>=8] and its complement is P[x<8]. Saves us a lot of work.\r<BR>\n" );
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document.write( "(1-.5833) +  (12 choose 8)*(.65)^8*(.35)^4 = .6534\r<BR>\n" );
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document.write( "c)P[6<=x<=10] = P[x=6]+P[x=7]+P[x=8]+P[x=9]+P[x=10]. Try to work this one out yourself. You should get .8730. </SPAN>\n" );
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