document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204602>Question 1204602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer knows that their items have a lengths that are skewed right, with a mean of 13.5 inches, and standard deviation of 3.4 inches.\r<BR>\n" );
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document.write( "If 46 items are chosen at random, what is the probability that their mean length is greater than 12.3 inches?<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 #840968 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=840968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x̄ = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.3+ ALIGN=MIDDLE  ALT=\"12.3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > => mean length\r<BR>\n" );
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document.write( "sample size <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=++46 ALIGN=MIDDLE  ALT=\"n=++46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "population mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=+13.5+ ALIGN=MIDDLE  ALT=\"mu=+13.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "standard deviation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma=+3.4 ALIGN=MIDDLE  ALT=\"sigma=+3.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " to find: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x̄ > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.3 ALIGN=MIDDLE  ALT=\"12.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "z-statistic:  (x̄ -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" >)/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sigma%2Fsqrt%28n%29%29 ALIGN=MIDDLE  ALT=\"%28sigma%2Fsqrt%28n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "compute z-statistic for x̄ = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.3+ ALIGN=MIDDLE  ALT=\"12.3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%2812.3+-+13.5%29%2F%283.4%2Fsqrt%2846%29%29+=+-2.393763523456 ALIGN=MIDDLE  ALT=\"z+=+%2812.3+-+13.5%29%2F%283.4%2Fsqrt%2846%29%29+=+-2.393763523456\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28z+%3E+-2.393763523456%29+=++0.99166175 ALIGN=MIDDLE  ALT=\"P%28z+%3E+-2.393763523456%29+=++0.99166175\"   DISABLED_style= \"max-width:90%; height:auto;\" >  =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99.166175 ALIGN=MIDDLE  ALT=\"99.166175\"   DISABLED_style= \"max-width:90%; height:auto;\" >% chance of the sample mean being greater than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.3+ ALIGN=MIDDLE  ALT=\"12.3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >inches long\r<BR>\n" );
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