document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151591>Question 1151591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A multiple-choice quiz has 200 questions, each with 4 possible answers, of which only 1 is the<BR>\n" );
document.write( "correct answer. What is the probability that sheer guesswork yields from 25 to 30 correct<BR>\n" );
document.write( "answers for 80 of 200 problems about which the student has no knowledge? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773593 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=773593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability of a correct answer is 1/4 so E(X) or mean is np or 20  (80*1/4)<BR>\n" );
document.write( "variance is np(1-p) or 20*0.75=15.5<BR>\n" );
document.write( "sd is sqrt (V)=3.94\r<BR>\n" );
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document.write( "guesswork between 25 and 30\r<BR>\n" );
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document.write( "normal approximation from 24.5 to 30.5 to include both 25 and 30 (continuity correction factor)\r<BR>\n" );
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document.write( "z=(24.5-20)/3.94=1.14<BR>\n" );
document.write( "z=(30.5-20)/3.94=2.66<BR>\n" );
document.write( "That probability is 0.1232\r<BR>\n" );
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document.write( "the exact probability is 0.1194.  Without the CCF, the calculated probability would be 0.0981 </SPAN>\n" );
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