document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927549>Question 927549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this question, please?\r<BR>\n" );
document.write( "\n" );
document.write( "Sugar packaged by a certain machine has a mean weight of 5 lb and a standard deviation of 0.03 lb. For what values of c can the manufacturer of the machinery claim that the sugar packaged by this machine has a weight between 5 &#8722; c and 5 + c lb with probability at least 91%?<BR>\n" );
document.write( "at least c = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563065 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=563065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are asked to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+ ALIGN=MIDDLE  ALT=\"W+\"   DISABLED_style= \"max-width:90%; height:auto;\" >denotes the weight of a package of sugar,\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%285-c+%3C+W+%3C5%2Bc+%29%3C=0.91 ALIGN=MIDDLE  ALT=\"P%285-c+%3C+W+%3C5%2Bc+%29%3C=0.91\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W ALIGN=MIDDLE  ALT=\"W\"   DISABLED_style= \"max-width:90%; height:auto;\" > is normally distributed, transform it into a *standard* normally distributed variable, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using the formula:\r<BR>\n" );
document.write( "\n" );
document.write( "Z=(W&#8722;&#956;)&#963; <=> W=Z&#963;+&#956;\r<BR>\n" );
document.write( "\n" );
document.write( "where &#956;  and &#963; are the mean and std. deviation of W's distribution.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%285-c+%3C0.03Z%2B5+%3C5%2Bc%29+%3C=0.91 ALIGN=MIDDLE  ALT=\"P%285-c+%3C0.03Z%2B5+%3C5%2Bc%29+%3C=0.91\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-c%2A0.03%3CZ%3Cc%2A0.03%29%3C=0.91 ALIGN=MIDDLE  ALT=\"P%28-c%2A0.03%3CZ%3Cc%2A0.03%29%3C=0.91\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-c%2A0.03%3CZ%3Cc%2A0.03%29%3C=0.91 ALIGN=MIDDLE  ALT=\"P%28-c%2A0.03%3CZ%3Cc%2A0.03%29%3C=0.91\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Due to the symmetry of the normal curve, you can write this as\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%3CZ%3Cc%2A0.03%29%3C=0.455 ALIGN=MIDDLE  ALT=\"P%280%3CZ%3Cc%2A0.03%29%3C=0.455\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28Z%3Cc%2A0.03%29-P%28Z%3C0%29%3C=0.455 ALIGN=MIDDLE  ALT=\"P%28Z%3Cc%2A0.03%29-P%28Z%3C0%29%3C=0.455\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28Z%3Cc%2A0.03%29-0.5%3C=0.455 ALIGN=MIDDLE  ALT=\"P%28Z%3Cc%2A0.03%29-0.5%3C=0.455\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28Z%3Cc%2A0.03%29%3C=0.955 ALIGN=MIDDLE  ALT=\"P%28Z%3Cc%2A0.03%29%3C=0.955\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Referring to a z-table, you get a corresponding z-value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.70 ALIGN=MIDDLE  ALT=\"1.70\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "In other words,\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28Z%3Cc%2A0.03%29%3C=0.955 ALIGN=MIDDLE  ALT=\"P%28Z%3Cc%2A0.03%29%3C=0.955\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <=>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28Z%3C1.70%29%3C=0.955 ALIGN=MIDDLE  ALT=\"P%28Z%3C1.70%29%3C=0.955\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.7=c%2A0.03 ALIGN=MIDDLE  ALT=\"1.7=c%2A0.03\"   DISABLED_style= \"max-width:90%; height:auto;\" >  => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=0.051 ALIGN=MIDDLE  ALT=\"c=0.051\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );