document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086135>Question 1086135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A brand name has a 60&#8203;% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 6 randomly selected consumers.<BR>\n" );
document.write( "   What is the probability that exactly 5 of the selected consumers recognize the brand&#8203; name?\r<BR>\n" );
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document.write( ". What is the probability that all of the selected consumers recognize the brand&#8203; name?\r<BR>\n" );
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document.write( "What is the probability that at least 5 of the selected consumers recognize the brand&#8203; name?\r<BR>\n" );
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document.write( "If 66 consumers are randomly&#8203; selected, is 55 an unusually high number of consumers that recognize the brand&#8203; name? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700305 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Exactly 5 is 6C5 (6 ways to choose them) (.6)^5*.4=6*.0311=0.187<BR>\n" );
document.write( "All of them is 0.6^6=0.047<BR>\n" );
document.write( "at least 5 is the sum of the first two or 0.234<BR>\n" );
document.write( "Can do it with normal approximation or binomial<BR>\n" );
document.write( "binomial is 66C55*.6^55*.4^11=0.000028<BR>\n" );
document.write( "normal has mean of 66*0.6=39.6<BR>\n" );
document.write( "sd is sqrt (66*0.6*0.4)=sqrt(15.84)=3.98<BR>\n" );
document.write( "do it greater than 54.5 for continuity correction.<BR>\n" );
document.write( "z>=(54.5-39.6)/3.98>=+3.74<BR>\n" );
document.write( "This probability is 0.00009.<BR>\n" );
document.write( "Yes, it would be an unusually high number of consumers.   </SPAN>\n" );
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