document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189824>Question 1189824</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7). Forty-five percent of the adult population in a particular large city are women. A court is to randomly select a jury of 12 adults from the population of all adults of this city.\r<BR>\n" );
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document.write( "a) Find the probability that none of the 12 jurors is a woman. (1 point)\r<BR>\n" );
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document.write( "b) Find the probability that at most 4 of the 12 jurors are women. (1 point)\r<BR>\n" );
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document.write( "c) Let x denote the number of women in 12 adults selected for this jury. Obtain the probability distribution of x. \r<BR>\n" );
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document.write( "d) Using the probability distribution obtained in part c, find the following probabilities.\r<BR>\n" );
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document.write( "i. P(x > 6)\r<BR>\n" );
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document.write( "ii. P(x<=3)\r<BR>\n" );
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document.write( "iii. P(2<= x<=7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821433 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=821433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability distribution for women, let them be x, is 12Cx(0.45)^x*(0.55)^(n-x)\r<BR>\n" );
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document.write( "a. this is 0.55^12 all men=0.0008<BR>\n" );
document.write( "for at most 4 are women--that is 0,1,2,3<BR>\n" );
document.write( "we know 0;<BR>\n" );
document.write( "1 is 12*0.45*0.55^11=0.0075<BR>\n" );
document.write( "2 is 12C2*0.45^2*0.55^10=0.0339<BR>\n" );
document.write( "3= 12C3*0.45^3*0.55^9=0.0923<BR>\n" );
document.write( "12C4*0,45^4*0.55^8=0.1700<BR>\n" );
document.write( "sum is 0.3045, the answer<BR>\n" );
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document.write( "p (x>6), can use calculator 1-binomcdf(12,0.45,6)=0.2607<BR>\n" );
document.write( "can check, since it is 1-(sum of prob. for 0-6)=1-0.3045-0.2225-0.1489=0.2606 (rounding difference) <BR>\n" );
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document.write( "x<=3, can use the above and it is 0.1345<BR>\n" );
document.write( "between 2 and 7<BR>\n" );
document.write( "less than 7-less than 2 =0.8883-0.0083=0.88<BR>\n" );
document.write( "can check<BR>\n" );
document.write( "for 5 12C5*0.45^5*0.55^7=0.2225<BR>\n" );
document.write( "for 6 it is 0.2124<BR>\n" );
document.write( "for 7 it is 0.1489<BR>\n" );
document.write( "between 2 and 7 inclusive it is 0.88<BR>\n" );
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