document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993926>Question 993926</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a bottle-filling process, the amount of drink injected into 16 oz bottles is normally distributed with a mean of 16 oz and a standard deviation of .32 oz. Bottles containing less than 15.86 oz do not meet the bottler’s quality standard. What percentage of filled bottles do not meet the standard? (Round the z value to 2 decimal places. Round your answer to 2 decimal places.)\r<BR>\n" );
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document.write( "  P(x < 15.86) 	%   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #613097 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=613097\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the z factor is equal to (x - m) / s\r<BR>\n" );
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document.write( "x is the raw score.<BR>\n" );
document.write( "m is the mean.<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "the critical z factor is the z-score of the cutoff value.\r<BR>\n" );
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document.write( "if the bottle contains less than 15.86 ounces of drink, then it is rejected.\r<BR>\n" );
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document.write( "that makes the cutoff z factor equal to (15.86 - 16) / .32 = -.44\r<BR>\n" );
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document.write( "look up a z-score of -.44 in the z-score table and you will get .33\r<BR>\n" );
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document.write( "that means that 33% of the z-scores in the normal distribution table are below a z-score of .44.\r<BR>\n" );
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document.write( "that means that 33% of the bottles would be rejected if the amount of drink in the bottles was normally distributed with a mean of 16 ounces and the cutoff was any bottle that had less than 15.86 ounces of drink in it.\r<BR>\n" );
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document.write( "you can see the results in the following z-score calculator outputs.\r<BR>\n" );
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document.write( "the first output is based on the raw score.\r<BR>\n" );
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document.write( "the second output is based on the z-score.\r<BR>\n" );
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document.write( "the different in percentage is due to rounding of the z-score.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/100203.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/100204.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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