document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145746>Question 1145746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A brand name has a 40​% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 5 randomly selected consumers. Complete parts​ (a) through​ (d) below.<BR>\n" );
document.write( "a. What is the probability that exactly 4 of the selected consumers recognize the brand​ name?<BR>\n" );
document.write( "The probability that exactly 4 of the 5 consumers recognize the brand name is <BR>\n" );
document.write( "0.131.<BR>\n" );
document.write( "​(Round to three decimal places as​ needed.)<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 #767003 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=767003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p(4) = .4^4 * .6^1 * c(5,4) = .0768 = .077\r<BR>\n" );
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document.write( "this is a binomial distribution type problem where p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "n is equal to 5<BR>\n" );
document.write( "x ranges from 0 to 5.<BR>\n" );
document.write( "c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "the following excel spreadsheet shows all the probabilities from x = 0 to x = 5.<BR>\n" );
document.write( "the sum of all the probabilities is equal to 1, as it should be.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/092503.jpg\" alt=\"$$$\" >\r<BR>\n" );
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