document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104256>Question 1104256</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.77.\r<BR>\n" );
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document.write( "How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719028 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=719028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.77. <BR>\n" );
document.write( "How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?<BR>\n" );
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document.write( "Find original standard deviation::<BR>\n" );
document.write( "mean = np*100*0.77 = 77<BR>\n" );
document.write( "std = sqrt(npq) = sqrt(77*0.23) = 4.104<BR>\n" );
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document.write( "New conditions.  Find \"n\".<BR>\n" );
document.write( "(4.104)/2 = sqrt(npq)<BR>\n" );
document.write( "2.052 = sqrt(n*0.77*0.23)<BR>\n" );
document.write( "4.211 = 0.1771n<BR>\n" );
document.write( "n = 24 when rounded up<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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