document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114947>Question 1114947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An archer is able to hit the bull's-eye 55% of the time. She will shoot 8 arrows. Let X = the number of arrows which hit the bulls - eye.<BR>\n" );
document.write( "a. For each of the requested probabilities: express the probability in terms of X, and find the probability. <BR>\n" );
document.write( "1. The probability that the archer hits the bulls - eye exactly 4 times.\r<BR>\n" );
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document.write( "2. The probability that she hits the bulls - eye no more than 5 times.\r<BR>\n" );
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document.write( "b. The mean of X is 4.4 arrows, but clearly, the archer cannot hit the target 4.4 times! please interpret this mean of X.\r<BR>\n" );
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document.write( "C. 1. Show a calculation which would giv the mean of X<BR>\n" );
document.write( "2. Find the standard deviation of X.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729854 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=729854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For 8 arrows<BR>\n" );
document.write( "p(4)=8C4*(0.55^4)(0.45)^4<BR>\n" );
document.write( "=70*0.0915*0.0410=0.0458<BR>\n" );
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document.write( "no more than 5<BR>\n" );
document.write( "do 6,7,8 and subtract from 1<BR>\n" );
document.write( "8 is 0.45^8=0.0017<BR>\n" );
document.write( "7 is 8C7*0.55*0.45^7=0.0164<BR>\n" );
document.write( "6 is 8C6*0.55^2*0.45^6=0.0703<BR>\n" );
document.write( "Those 3 add to 0.0884<BR>\n" );
document.write( "Subtract from 1 and the answer is 0.916 probability.<BR>\n" );
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document.write( "The expected value is 4.4, which means if this is performed an infinite number of times, the average will be 4.4<BR>\n" );
document.write( "The E(X)=x*p(x)=8*0.55=4.4<BR>\n" );
document.write( "V(X)=np(1-p)=4.4*0.45=1.98<BR>\n" );
document.write( "SD is sqrt (V(X))=1.41<BR>\n" );
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