document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203023>Question 1203023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40%<BR>\n" );
document.write( " of this population prefers the color green. If 20<BR>\n" );
document.write( " buyers are randomly selected, what is the probability that exactly a fifth of the buyers would prefer green? Round your answer to four decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838259 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=838259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = .4<BR>\n" );
document.write( "q = 1 - .4 = .6<BR>\n" );
document.write( "n = 20<BR>\n" );
document.write( "p(x) = p^x * q^(n-x) * c(n,x)<BR>\n" );
document.write( "when since 1/5 of 20 = 4, the formula becomes:<BR>\n" );
document.write( "p(4) = .4^4 * .6^16 * c(20,4) = .03499.<BR>\n" );
document.write( "that becomes 3.499% which rounds to 3.5%.\r<BR>\n" );
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document.write( "c(n,x) is equal to n! / (x! * (n-x)!)<BR>\n" );
document.write( "that becomes 20! / (4! * 16!)<BR>\n" );
document.write( "that becoms (20*19*18*17*16!) / (4! * 16!)<BR>\n" );
document.write( "that becomes (20*19*18*17) / (4*3*2*1) which is equal to 4845<BR>\n" );
document.write( "p(4) becomes equal to .4^4 * .6^16 * 4845 = .03499 rounded to 5 decimal digits.\r<BR>\n" );
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document.write( "i calculated the total probabilities in excel.<BR>\n" );
document.write( "hare are the results.<BR>\n" );
document.write( "the sum of all the proabilities equals 1, as it should.<BR>\n" );
document.write( "here are the results.\r<BR>\n" );
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