document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=352363>Question 352363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The amount of fill in a half liter soft drink bottle is normally distributed. The process has a std. deviation of 5 ml. The mean is adjustable. a) Where should the mean be set to ensure a 95 percent probability that a half liter bottle will not be underfilled? b) A 99 percent probability? c) A 99.9 percent probability? Explain.<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 #251955 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=251955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The amount of fill in a half liter soft drink bottle is normally distributed. The process has a std. deviation of 5 ml. The mean is adjustable. <BR>\n" );
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document.write( "a) Where should the mean be set to ensure a 95 percent probability that a half liter bottle will not be underfilled? <BR>\n" );
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document.write( "A value that is 1.645 std below the mean will have 95% of the data above it.<BR>\n" );
document.write( "1.645*5ml = 8.2243ml<BR>\n" );
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document.write( "1/2 liter = 500 ml<BR>\n" );
document.write( "500-8.2243 = 491.78ml<BR>\n" );
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document.write( "Set the mean at 491.78ml\r<BR>\n" );
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document.write( "b) A 99 percent probability? <BR>\n" );
document.write( "Same as above but use z value of 2.326. That z will have 99% above it.\r<BR>\n" );
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document.write( "c) A 99.9 percent probability? Explain.<BR>\n" );
document.write( "Same as above but use z value of 3.09.  That will have 99.9% above it.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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