document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086323>Question 1086323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Last year I ran in a 10K where the average completion time was 48.1 min with a standard deviation of 6.2 min. This year, runners completed the race in an average of 45.7 min with a 7.8 min standard deviation. The distribution of running times each year was approximately normal. <BR>\n" );
document.write( "a. If I completed the race in 46.0 min last year and in 43.2 minutes this year, in which year did I run a better race as compared to the rest of the field? \r<BR>\n" );
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document.write( "b.	If 6578 runners were in this year’s race, how many runners beat my time? \r<BR>\n" );
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document.write( "c.	What time would have gotten me into the top 25%  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700495 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Calculate the z scores for both races.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B1%5D=+%2846-48.1%29%2F6.2+ ALIGN=MIDDLE  ALT=\"z%5B1%5D=+%2846-48.1%29%2F6.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B2%5D=+%2843.2-45.7%29%2F7.8+ ALIGN=MIDDLE  ALT=\"z%5B2%5D=+%2843.2-45.7%29%2F7.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The lower the z score, the better the placement.<BR>\n" );
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document.write( "b) Find the probability using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B2%5D ALIGN=MIDDLE  ALT=\"z%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > then multiply that value by the number of runners. Run up or down appropriately. <BR>\n" );
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document.write( "c) Find z such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28z%5B25%5D%29=0.25 ALIGN=MIDDLE  ALT=\"P%28z%5B25%5D%29=0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28z%5B25%5D%29=0.25 ALIGN=MIDDLE  ALT=\"P%28z%5B25%5D%29=0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B25%5D+=-0.67449+ ALIGN=MIDDLE  ALT=\"z%5B25%5D+=-0.67449+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28X%5B25%5D-45.7%29%2F7.8+=-0.67449+ ALIGN=MIDDLE  ALT=\"%28X%5B25%5D-45.7%29%2F7.8+=-0.67449+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5B25%5D ALIGN=MIDDLE  ALT=\"X%5B25%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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