document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051786>Question 1051786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From past experience, a company found that in cartons of DVDs, 90% contain no defective DVDs, 5% contain one defective DVD, 3% contain two defective DVDs, and 2% contain three defective DVDs. Find the mean, variance, and standard deviation for the number of defective DVDs. Please explain all steps.<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667271 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=667271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x====0====1====2====3<BR>\n" );
document.write( "p(x)0.9=0.05 0.03==0.02<BR>\n" );
document.write( "E(x), the mean is x*p(x)=0+0.05+0.06+0.06=0.17 defect per carton.<BR>\n" );
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document.write( "variance is the average (here, a weighted average) of the squared deviations of the mean.  This is [x-E(x)]^2*p(x)\r<BR>\n" );
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document.write( "0.17^2*0.90=0.0260<BR>\n" );
document.write( "0.83^2*0.05=0.0344<BR>\n" );
document.write( "1.83^2*0.03=0.1098<BR>\n" );
document.write( "2.83^2*0.02=0.1602<BR>\n" );
document.write( "Sum is 0.3304 defective^2/box^2<BR>\n" );
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document.write( "Standard deviation is sqrt(V(x))=0.5748 defective/box </SPAN>\n" );
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