document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193397>Question 1193397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Fifty percent of midsize manufacturers planned to have management representative visit Canada and Mexico to take advantage of opportunities created by the North American Free Trade Agreements. An export-import group in Toronto , Canada , has invited 20 US midsize manufacturers to participate in the conference to explore trade opportunities. What is the probability that 12 or more of these manufacturers will send representatives? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825419 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>0.251722 (approximate)</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "x = number of successes = number of companies that send a representative<BR>\n" );
document.write( "n = sample size = 20<BR>\n" );
document.write( "p = probability a company sends a representative = 50% = 0.5\r<BR>\n" );
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document.write( "B(x) = binomial probability<BR>\n" );
document.write( "B(x) = (n C x)*(p)^(x)*(1-p)^(n-x)<BR>\n" );
document.write( "B(x) = (20 C x)*(0.5)^(x)*(1-0.5)^(20-x)<BR>\n" );
document.write( "B(x) = (20 C x)*(0.5)^(x)*(0.5)^(20-x)<BR>\n" );
document.write( "The n C x refers to the nCr combination formula.\r<BR>\n" );
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document.write( "Plug in x = 12<BR>\n" );
document.write( "B(x) = (20 C x)*(0.5)^(x)*(0.5)^(20-x)<BR>\n" );
document.write( "B(12) = (20 C 12)*(0.5)^(12)*(0.5)^(20-12)<BR>\n" );
document.write( "B(12) = (125,970)*(0.5)^(12)*(0.5)^(8)<BR>\n" );
document.write( "B(12) = 0.120134 approximately<BR>\n" );
document.write( "This is the approximate probability exactly twelve companies send a representative.\r<BR>\n" );
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document.write( "Repeat for x = 13<BR>\n" );
document.write( "B(x) = (20 C x)*(0.5)^(x)*(0.5)^(20-x)<BR>\n" );
document.write( "B(13) = (20 C 13)*(0.5)^(13)*(0.5)^(20-13)<BR>\n" );
document.write( "B(13) = (77,520)*(0.5)^(13)*(0.5)^(7)<BR>\n" );
document.write( "B(13) = 0.073929 approximately<BR>\n" );
document.write( "This is the approximate probability exactly thirteen companies send a representative.\r<BR>\n" );
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document.write( "These steps are repeated for x = 14, x = 15, all the way up to x = 20\r<BR>\n" );
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document.write( "I'll let you do those steps, but you should get these approximate results:<BR>\n" );
document.write( "B(14) = 0.036964<BR>\n" );
document.write( "B(15) = 0.014786<BR>\n" );
document.write( "B(16) = 0.004621<BR>\n" );
document.write( "B(17) = 0.001087<BR>\n" );
document.write( "B(18) = 0.000181<BR>\n" );
document.write( "B(19) = 0.000019<BR>\n" );
document.write( "B(20) = 0.000001<BR>\n" );
document.write( "All of which are approximate to 6 decimal places.\r<BR>\n" );
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document.write( "The last step is to add B(12), B(13), all the way up to B(20)<BR>\n" );
document.write( "You should get <font color=red>0.251722</font> when doing so.<BR>\n" );
document.write( "There's about a 25.1722% chance of twelve or more companies sending a representative.\r<BR>\n" );
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document.write( "Here's one free calculator to check your work<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://calculator-online.net/binomial-distribution-calculator/\">https://calculator-online.net/binomial-distribution-calculator/</a><BR>\n" );
document.write( "there are tons of other free options out there as well.<BR>\n" );
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