document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=427216>Question 427216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The weight of food packed in certain containers has a mean of 16 ounces and a standard deviation of 0.6 ounces. There are 36 containers placed in a box for shipping. Find the probability that a randomly picked box will weight over 580 ounces. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297132 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=297132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let X = r.v. representing the weight of certain containers.<BR>\n" );
document.write( "Then the distribution in question is Y = 36X.  This is also a normal distribution with mean E(Y) = E(36X) = 36E(X) = 36*16 = 576, and variance Var(Y) = Var(36X) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%5E2Var%28X%29+=+1296Var%28X%29+=+1296%280.6%29%5E2 ALIGN=MIDDLE  ALT=\"36%5E2Var%28X%29+=+1296Var%28X%29+=+1296%280.6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 466.56.  The standard deviation is thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28466.56%29+=+21.6 ALIGN=MIDDLE  ALT=\"sqrt%28466.56%29+=+21.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You're looking for the probability <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28Y+%3E+580%29+=+P%28Z+=+%28Y+-+576%29%2F21.6+%3E+%28580+-+576%29%2F21.6+=+0.185%29 ALIGN=MIDDLE  ALT=\"P%28Y+%3E+580%29+=+P%28Z+=+%28Y+-+576%29%2F21.6+%3E+%28580+-+576%29%2F21.6+=+0.185%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or P(Z > 0.185).  Now use any table of standard normal probabilities. </SPAN>\n" );
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