document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164705>Question 1164705</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a certain large university the weight of the male students and female<BR>\n" );
document.write( "students are approximately normally distributed with means and standard<BR>\n" );
document.write( "deviations of 180, and 20, and 130 and 15, respectively. If a male and female<BR>\n" );
document.write( "are selected at random, what is the probability that the sum of their weights<BR>\n" );
document.write( "is less than 280? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789208 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=789208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the means are 180 and 130<BR>\n" );
document.write( "the variances are 400 and 225 (square sd)<BR>\n" );
document.write( "the new distribution has mean of 310, the sum<BR>\n" );
document.write( "and variance 625, the sum of the individual variance, which means the sd for the combined distribution is 25\r<BR>\n" );
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document.write( "so probability sum of the weights is less than 280 is <BR>\n" );
document.write( "z<(280-310)/25<BR>\n" );
document.write( "z< -30/25 or -1.2<BR>\n" );
document.write( "probability=0.1151 </SPAN>\n" );
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