document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131012>Question 1131012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve this binomial distribution? The fewer than is throwing me off. I do not have the calculator for this but I do have access to Excel.\r<BR>\n" );
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document.write( "If 15 students from the special programs are randomly selected, find the probability that fewer than 10 of them graduated (graduation rate is 84% for students admitted through the special programs). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747826 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=747826\">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( "You want\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P\({r}<{10},15,0.84\)\ =\ \sum_{r=0}^9\,\(0.84\)^r\(0.16\)^{15-r}\">\r<BR>\n" );
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document.write( "So use the Excel formula\r<BR>\n" );
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document.write( "=BINOMDIST(9,15,0.84,TRUE)\r<BR>\n" );
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document.write( "9 is the number of successes, 15 is the number of trials, 0.84 is the probability of success on any given trial and the TRUE parameter makes it cumulative so that you are summing the probabilities for all of the numbers of successes from 0 to 9, i.e. all of the possibilities less than 10.\r<BR>\n" );
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document.write( "By the way, if you have a later model of Excel, you can also use BINOM.DIST with the same parameters.  Also, if you want the probability of 10 or more successes, use =1 - BINOMDIST(9,15,0.84,TRUE)<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( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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