document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052231>Question 1052231</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 53% of all persons in the U.S. population have at least some college education. Choose 10 persons at random. Find the probability that at least 5 do not have any college education. <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 #667676 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=667676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability that a person, chosen at random, has some college education is .53.\r<BR>\n" );
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document.write( "this means the probability that a person, chosen at random, does not have some college education is .47.\r<BR>\n" );
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document.write( "out of 10 people, you want to know the probability that at least 5 do not have a college education.\r<BR>\n" );
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document.write( "you would use the binomial probability formula, which 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( "set p equal the probability that the person does not have any college education.\r<BR>\n" );
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document.write( "that makes p = .47\r<BR>\n" );
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document.write( "set q equal the probability that the person does have some college education.\r<BR>\n" );
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document.write( "that makes q = 1 - .47 = .53.\r<BR>\n" );
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document.write( "p(x) will now give you the probability that x persons do not have any college education.\r<BR>\n" );
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document.write( "if you want to know if at least 5 do not have any college education, then you want to find the sum of p(x) for x = 5 to x = 10.\r<BR>\n" );
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document.write( "the probability that at least 5 do not have any college education is equal to 0.547373025.\r<BR>\n" );
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document.write( "the attached spreadsheet shows the calculations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/101102.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "this is the sum of p(x) for x = 5 to 10.\r<BR>\n" );
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document.write( "as an example of one of the calculations, let's use p(x) for x = 8.\r<BR>\n" );
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document.write( "the formula is p(x) = c(n,x) * p^x * q^(n-x)\r<BR>\n" );
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document.write( "when n = 10 and x = 8, this formula becomes p(8) = c(10,8) * .47^8 * .53^2.\r<BR>\n" );
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document.write( "since c(10,8) is equal to 10! / (8! * 2!) which is equal to 45, then:\r<BR>\n" );
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document.write( "p(8) = c(10,8) * .47^8 * .53^2 becomes p(8) = 45 * .47^8 * .53^2 which becomes p(5) = 0.030098657\r<BR>\n" );
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document.write( "you would manually do the same calculations for p(5), p(6), p(7), p(8), p(9), p(10).\r<BR>\n" );
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document.write( "alternatively, you can use excel.\r<BR>\n" );
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document.write( "there are also online binomial probability calculators that can do the work for you.\r<BR>\n" );
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document.write( "you just have to make sure you input the correct variables for the calculator to work.\r<BR>\n" );
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document.write( "one such calculator can be found here.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://stattrek.com/online-calculator/binomial.aspx\" target = \"_blank\">http://stattrek.com/online-calculator/binomial.aspx</a>\r<BR>\n" );
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document.write( "a picture of my inputs and outputs from this calculator are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/101103.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you would look for x >= 5 in this calculator.\r<BR>\n" );
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