document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261695>Question 261695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company specialises in packing of washing powder for a national chain of supermarkets.The machine used to pack the washing powder is calibrated to pack a mean of 510g.However,the packing machine is 100% reliable and there is some variation in the mean.The variability as measured by the standrd deviation is 2.5g.It is also known that the weight packed by the machine follows a normal distribution.The supermarket chain has recently been complaining because they think that too many washing powder boxes are either underweight or overweight.\r<BR>\n" );
document.write( "\n" );
document.write( "a)What is the percentage of the bags filled by the machine will weigh less that 507.5g?<BR>\n" );
document.write( "b)What is the probability that a bag filled by the machine weighs less than 512g?<BR>\n" );
document.write( "c)What percentage of the bags will weigh between 512 and 515g? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192800 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=192800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A company specialises in packing of washing powder for a national chain of supermarkets.<BR>\n" );
document.write( "The machine used to pack the washing powder is calibrated to pack a mean of 510g.<BR>\n" );
document.write( "However,the packing machine is not 100% reliable and there is some variation in the mean.The variability as measured by the standrd deviation is 2.5g.<BR>\n" );
document.write( "It is also known that the weight packed by the machine follows a normal distribution.The supermarket chain has recently been complaining because they think that too many washing powder boxes are either underweight or overweight. <BR>\n" );
document.write( "a)What is the percentage of the bags filled by the machine will weigh less that 507.5g?<BR>\n" );
document.write( "z(507.5) = (507.5-510)/2.5 = -1<BR>\n" );
document.write( "P(x<507.5) = P(z<-1) = 0.1587 = 15.87%<BR>\n" );
document.write( "--------------------------------------------------<BR>\n" );
document.write( "b)What is the probability that a bag filled by the machine weighs less than 512g?<BR>\n" );
document.write( "z(512) = (512-510)/2.5 = 0.8<BR>\n" );
document.write( "P(x<512) = P(z<0.8) = 0.7881 = 78.81%<BR>\n" );
document.write( "===========================================<BR>\n" );
document.write( "c)What percentage of the bags will weigh between 512 and 515g?<BR>\n" );
document.write( "Find the z-scores then find the % of population between those<BR>\n" );
document.write( "scores.  I get 18.91% using a TI calculator.<BR>\n" );
document.write( "===============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );