document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=384378>Question 384378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The mean diameter of a CD disc is 12.0 cm, produced by a company called \"Cardinal Best Compact Disk\", with a standard deviation of 0.012. CD's that are more than one standard deviation from the mean cannot be shipped. How can a quality control engineer use these statistics to help the company produce CD's that can be shipped? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #272121 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=272121\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that the diameters are normally distributed.  The z-score formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28X+-+mu%29%2Fsigma ALIGN=MIDDLE  ALT=\"z+=+%28X+-+mu%29%2Fsigma\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or vice-versa, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+mu+%2B+z%2Asigma ALIGN=MIDDLE  ALT=\"X+=+mu+%2B+z%2Asigma\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Within 1 sd, he can accept only  diameter values within the interval [12.0 - 0.012, 12.0 + 0.012] = [11.988, 12.012].  There is 100% - 68.26%  = 31.74% chance that a CD disc diameter is outside this interval.  (The z-score tells us how many sd's X is away from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" >.) </SPAN>\n" );
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