document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124808>Question 1124808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that 64% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:\r<BR>\n" );
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document.write( "a.	There are some lefties (&#8805; 1) among the 5 people. \r<BR>\n" );
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document.write( "b.	There are exactly 3 lefties in the group. \r<BR>\n" );
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document.write( "c.	There are at least 4 lefties in the group. \r<BR>\n" );
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document.write( "d.	There are no more than 2 lefties in the group. \r<BR>\n" );
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document.write( "e.	How many lefties do you expect? \r<BR>\n" );
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document.write( "f.	With what standard deviation?\r<BR>\n" );
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document.write( "Please help I am very confused! Especially with the problem E and A.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741352 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=741352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Some lefties (greater than or equal to 1) has probability 1- no lefties, or 1-.64^5=0.8926\r<BR>\n" );
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document.write( "Exactly 3 is 5C3*0.64^3*0.36^2, the 5C3 being number of ways (10) to choose 3 from 5.<BR>\n" );
document.write( "probability is 0.3397\r<BR>\n" );
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document.write( "Exactly 4 is 5*0.64^4*0.36=0.3020<BR>\n" );
document.write( "Exactly 5 is 0.64^5=0.1074<BR>\n" );
document.write( "Exactly 2 is 10*0.64^2*0.36^3=0.1911<BR>\n" );
document.write( "Exactly 1 is 5*.64*.36^4=0.0537<BR>\n" );
document.write( "0 is .36^5=0.0060\r<BR>\n" );
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document.write( "Using these, at least 4 includes 4 or 5. and that has probability 0.4094\r<BR>\n" );
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document.write( "no more than 2 means 0,1,2, and that probability is 0.2508\r<BR>\n" );
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document.write( "Expected value is n*p or 5*0.64=3.2<BR>\n" );
document.write( "sd is sqrt (variance), and variance is np(1-p)=3.2*0.36=1.152.  sqrt (1.152)=1.07, the sd. </SPAN>\n" );
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