document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051715>Question 1051715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello:\r<BR>\n" );
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document.write( "I can solve the following using the formula but cannot figure out how to do this problem using the binomial table.\r<BR>\n" );
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document.write( "Approximately 10% of American High School students drop out of school before graduation. Choose 10 students entering High School at random. Find the probability that at least 6 will graduate. Meaning P(graduating) = 100%-10% = 90% or p = .90 = 90% or p=.90 I changed it from 10.3% to 10% so p is 90% or .90, so that you can use the table to find the answer instead of the formula. Remember use 90% and use the table in the back of the text, Table B, not the formula for this one.\r<BR>\n" );
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document.write( "I understand that (6 <= x < 10)\r<BR>\n" );
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document.write( "The book gives X = .001  (is this the probability \r<BR>\n" );
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document.write( "How did they get .001 for X\r<BR>\n" );
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document.write( "How did they get q = 0.1\r<BR>\n" );
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document.write( "Did X = 5 come from the fact that x = 6, 7, 8, 9, 10\r<BR>\n" );
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document.write( "Help is greatly appreciated\r<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 #667178 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667178\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your problem states that 10% of american high school students drop out before graduation.\r<BR>\n" );
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document.write( "this means that 90% will graduate.\r<BR>\n" );
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document.write( "when you take a sample of 10 students out of the population and you want to know the probability that 6 or more out of the 10 will graduate, then you are most likely looking at a binomial probability.\r<BR>\n" );
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document.write( "the binomial probability is used when you either have success or failure and nothing in between\r<BR>\n" );
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document.write( "success in this case is the probability that the student will graduate.\r<BR>\n" );
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document.write( "failure im this case is the probability that the student will not graduate.\r<BR>\n" );
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document.write( "since there are only two probabilities total, the probability of failure is always 1 minus the probability of success.\r<BR>\n" );
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document.write( "similarly, since there are only two probabilities total, the probability of success is always 1 minus the probability of failure.\r<BR>\n" );
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document.write( "since the probability of success is the probability that the students will graduate, then p = probability of success = .9.\r<BR>\n" );
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document.write( "since the probability of failure is the probability that the students will not graduate (drop out), then q = .1.\r<BR>\n" );
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document.write( "the binomial formula is:\r<BR>\n" );
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document.write( "p(x) = c(n,x) * p^x * q^(n-x).\r<BR>\n" );
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document.write( "c(n,x) is the combination formula of n! / (x! * (n-x)!).\r<BR>\n" );
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document.write( "the sum of all probabilities always has to be equal to 1.\r<BR>\n" );
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document.write( "i used excel to calculate all the probabilities of p(x) from x = 0 to x = 10.\r<BR>\n" );
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document.write( "the result are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/101101.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can see from this table, that the probability of getting AT LEAST 6 out of the 10 students, chosen at random from the general population, to be among the 10% of the general population that will drop out is 0.998365063, which is equal to .998 if you round to 3 decimal places.\r<BR>\n" );
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document.write( "what you do is you calculate for p(6), p(7), p(8), p(9), p(10).<BR>\n" );
document.write( "you then add them up to get the probability of p(x) from x = 6 to 10.<BR>\n" );
document.write( "that becomes the probability that at least 6 out of the 10 students will graduate.\r<BR>\n" );
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document.write( "here's a reference on binomial probability that might help you to understand.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"http://www.regentsprep.org/regents/math/algtrig/ats7/blesson.htm\" target=\"_blank\">http://www.regentsprep.org/regents/math/algtrig/ats7/blesson.htm</a> </SPAN>\n" );
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