document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171776>Question 1171776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let X be N(100, 10) and Y be N(10, 5). What is P(X − 4Y > 40) \r<BR>\n" );
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document.write( "I think 4Y is N(40,20) but that gives me a negative value for the standard deviation of X-4Y. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796689 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=796689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Need to assume these are independent. <BR>\n" );
document.write( "x is N~ (100,10) using variance<BR>\n" );
document.write( "4y is N~(40, 80) because the constant*the variance is c^2*var(N) or 16*5=80<BR>\n" );
document.write( "the distribution would be (60, 90), because when the two are combined, the variances are added, even when one distribution is subtracted from another. There is more variability when there is combining. <BR>\n" );
document.write( "The sd is 9.486<BR>\n" );
document.write( "z > (60-40)/9.486 or > 2.108 <BR>\n" );
document.write( "probability is  0.0175 </SPAN>\n" );
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