document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132398>Question 1132398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A machine is used to regulate the amount of dye dispensed for mixing shades of paint. Suppose the amount of dye dispensed per paint can is normally distributed with a mean of 6 ml and a standard deviation of 0.4 ml. \r<BR>\n" );
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document.write( "a)	What proportion of paint cans will have more than 6.5 ml of dye?\r<BR>\n" );
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document.write( "b)	Find the amount of dye that the bottom 2% of paint cans have less than.\r<BR>\n" );
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document.write( "c)	Suppose that new quality control procedures are introduced that lower the standard deviation from 0.4 to a new value  (the mean is still 6 ml). With this new standard deviation, we are told that 98% of the paint cans contain between 5.5 and 6.5 ml of dye. Calculate the standard deviation.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749688 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=749688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( "z>(6.5-6)/0.4 or z>1.25.  This has probability of 0.1056<BR>\n" );
document.write( "probability is 0.02 at -2.055<BR>\n" );
document.write( "-2.055=(x-6)/0.4<BR>\n" );
document.write( "x-6=-.822<BR>\n" );
document.write( "x=5.178 ml; anything less is the bottom 2%<BR>\n" );
document.write( "now-2.055=(-5.5-6)/sd; -2.055=-.5/sd<BR>\n" );
document.write( "sd=-.5/-2.055=0.2433 or 0.24<BR>\n" );
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