document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052174>Question 1052174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Shipping line W deals with transportation of goods in containers of various sizes. Charges for each container depend on its weight. A consignment of 800 containers in a particular vessel is in the high seas. Records indicate that the weights are normally distributed. The chances of a container weighing more than 20 tonnes are 97,72% while the chances of a container weighing less than 42,55 tonnes are 99,4%.\r<BR>\n" );
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document.write( "(1) Determine the mean µ and the standard deviation of the weights of the containers.\r<BR>\n" );
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document.write( "(2) Charges of one tonne are £2,50. Determine the number of containers whose weights are more than the mean µ but not exceeding 32,2 tonnes. Hence or otherwise, determine the total charges on these containers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667601 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> : Shipping line W deals with transportation of goods in containers of various sizes. Charges for each container depend on its weight. <BR>\n" );
document.write( "A consignment of 800 containers in a particular vessel is in the high seas. Records indicate that the weights are normally distributed. <BR>\n" );
document.write( "The chances of a container weighing more than 20 tonnes are 97.72% while the chances of a container weighing less than 42.55 tonnes are 99.4%. <BR>\n" );
document.write( "(1) Determine the mean µ and the standard deviation of the weights of the containers.<BR>\n" );
document.write( "z-value with a left tail of 1-0.9772 = 0.0228:: z = invNorm(0.0228)= -2<BR>\n" );
document.write( "z-value with a left tail of 0.994 :: z = invNorm(0.994) = 2.5<BR>\n" );
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document.write( "Use x = z*s + u<BR>\n" );
document.write( "20 = -2*s + u<BR>\n" );
document.write( "42.55 = 2.5s + u<BR>\n" );
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document.write( "Subtract and solve for \"s\"::<BR>\n" );
document.write( "22.55 = 4.5s<BR>\n" );
document.write( "s = 5<BR>\n" );
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document.write( "Solve for \"u\"::<BR>\n" );
document.write( "20 = -2*5 + u<BR>\n" );
document.write( "u = 30<BR>\n" );
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document.write( "(2) Charges of one tonne are £2,50. Determine the number of containers whose weights are more than the mean µ but not exceeding 32.2 tonnes. Hence or otherwise, determine the total charges on these containers.<BR>\n" );
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document.write( "z(32.2) = (32.2-30)/5 = 2.2/5 = 0.44<BR>\n" );
document.write( "P(30< x < 32.2) = P(0< z <0.44) = normalcdf(0,0.44) = 17%<BR>\n" );
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document.write( "Charge = 0.17*800*2.5 = L340.06<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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