document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=764365>Question 764365</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A quiz consists of 15 multiple choice questions. Each question has 5 choices, with exactly one correct choice. A student, totally unprepared for the quiz, guesses on each of the 15 questions.\r<BR>\n" );
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document.write( "	a.	How many questions should the student expect to answer correctly? \r<BR>\n" );
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document.write( "	b.	What is the standard deviation of the number of questions answered correctly?<BR>\n" );
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document.write( "	c.	If at least 9 questions must be answered correctly to pass the quiz, what is the chance the student passes? <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 #465392 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=465392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "a.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \mu_X\ =\ np\ =\ 15\,\cdot\,0.2\">\r<BR>\n" );
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document.write( "b.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sigma_X\ =\ \sqrt{np(1\,-\,p)}\">\r<BR>\n" );
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document.write( "c.  You need the probability that the student will score exactly 9 plus the probability of exactly 10 plus the probability of exactly 11, and so on all the way up to 15.\r<BR>\n" );
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document.write( "The probability of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> trials where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is the probability of success on any given trial is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(n;k,p)\ =\ {{n}\choose{k}}\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k}\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE {{n}\choose{k}}\"> is the number of combinations of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> things taken <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> at a time and is calculated by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{n!}{k!(n\,-\,k)!}\">\r<BR>\n" );
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document.write( "You need to calculate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(15;\geq 9,0.2)\ =\ \sum_{i=9}^{15}\,{{15}\choose{i}}\left(0.2\right)^i\left(0.8\right)^{n\,-\,i}\">\r<BR>\n" );
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document.write( "You can do your own arithmetic.  My Kentucky Windage estimate: Mighty slim <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ >\ P(\geq 9)\ >\ \ \"> none.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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