document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073050>Question 1073050</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to get a simplified breakdown of how to solve this equation without using a calculator?\r<BR>\n" );
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document.write( "56% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four.\r<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 #687883 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=687883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Without a calculator, this is difficult, because even the approximation of 50% is not too accurate.<BR>\n" );
document.write( "One could use a normal approximation which barely makes the assumptions valid.<BR>\n" );
document.write( "E(x)=5.6, and V(x)=5.6*0.44=0.2464, almost 0.25, so sd is 0.5<BR>\n" );
document.write( "5 would be about 1 sd to the left (1.2 sd exactly) and about 0.31 or a little more<BR>\n" );
document.write( "at least 6 would be everything to the right of z=0.8, which is a little less than 0.75.<BR>\n" );
document.write( "less than 4 would be z< 3.1 sd and this would be expected to be near 0. The true values are considerably different:<BR>\n" );
document.write( "The exact number is 10C5(0.56)^5(0.44)^5<BR>\n" );
document.write( "This is not too dissimilar from getting 5 heads in 10 coin tosses.<BR>\n" );
document.write( "That is 252*(1/1024) or about a quarter.  The exact answer is 0.2289<BR>\n" );
document.write( "For at least 6, it would more, but the values of 5,4,3,2,1,0 would not be relevant 0.2427+0.1765+0.0843+0.0238+0.003, or 0.5276<BR>\n" );
document.write( "For less than 4, it would be 3,2,1,0 and those probabilities are roughly 175/1024, a little less, since the probability of 0.44 is less than 0.50 that I am using to estimate.<BR>\n" );
document.write( "0.0002+0.0035+0.0198+0.0672+=0.0907 </SPAN>\n" );
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