document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965490>Question 965490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> *****Of all the trees planted by a landscaping firm, 55% survive. What is the probability that 12 or more of the 14 trees they just planted will survive? \r<BR>\n" );
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document.write( "(Use a table of binomial probabilities. Give your answer correct to four decimal places.)\r<BR>\n" );
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document.write( "I have been stuck on this for days!!  Please help me.  If possible please show step-by-step instructions.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590160 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=590160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 55% survive, so p = .55<BR>\n" );
document.write( "this means that 45% don't survive.<BR>\n" );
document.write( "q = 1 - p = 1 - .55 = .45\r<BR>\n" );
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document.write( "you have p = .55<BR>\n" );
document.write( "you have q = .45\r<BR>\n" );
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document.write( "the binomial probability 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( "x represents the ratio of plants that survive.<BR>\n" );
document.write( "n is the total number of trees that were planted.<BR>\n" );
document.write( "p(x) is the probability that x will survive.<BR>\n" );
document.write( "c(n,x) is the number of possible combinations of n plants taken x at a time where order is not important.<BR>\n" );
document.write( "c(n,x) is defined as n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "you want to know the probability that 12 or more will survice.\r<BR>\n" );
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document.write( "this is equal to the probability that exactly 12 will survive plus the probability that exactly 13 will survice plus the probability that exactly 14 will survive.\r<BR>\n" );
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document.write( "so you need to find p(12) + p(13) + p(14).\r<BR>\n" );
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document.write( "p(12) = c(14,12) * p^12 * q^2 = 91 * .55^12 * .45^2 = .0141194797\r<BR>\n" );
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document.write( "p(13) = c(14,13) * p^13 * q^1 = 14 * .55^13 * .45^1 = .0026549449\r<BR>\n" );
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document.write( "p(14) = c(14,14) * p^14 * q^0 = 1 * .55^14 * .45^0 = .0002317809043\r<BR>\n" );
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document.write( "p(12) + p(13) + p(14) = .0170062055\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "here's one of the combination calculations to show you how they're done.\r<BR>\n" );
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document.write( "c(14,12) = 14! / (12! * 2!) = (14 * 13 * 12!) / (12! * 2!) = (14 * 13) / 2! = 7 * 13 = 91.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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