document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196427>Question 1196427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Finishing times in the annual cross country meet hosted by Altoona High School have a symmetrical distribution with a mean of 22.7 minutes and a standard deviation of 3.22 minutes.\r<BR>\n" );
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document.write( "What number would correctly complete the sentence below?\r<BR>\n" );
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document.write( "Approximately 16% of the runners in the Altoona High School cross country meet have finishing times below _____ minutes.  Round your answer to one decimal place.<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 #829247 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "According to the Empirical rule, roughly 68% of the population from a normal distribution is between z = -1 and z = 1<BR>\n" );
document.write( "I.e. about 68% of the population is within 1 standard deviation of the mean.\r<BR>\n" );
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document.write( "P(-1 < z < 1) = 0.68 approximately<BR>\n" );
document.write( "This leaves 1-0.68 = 0.32 as the area of the two tails combined<BR>\n" );
document.write( "P(z < -1 or z > 1) = 0.32 approximately\r<BR>\n" );
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document.write( "One tail is 0.32/2 = 0.16<BR>\n" );
document.write( "About 16% of the area is to the left of z = -1<BR>\n" );
document.write( "P(z < -1) = 0.16 approximately\r<BR>\n" );
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document.write( "mu = 22.7 = mean<BR>\n" );
document.write( "sigma = 3.22 = standard deviation\r<BR>\n" );
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document.write( "Let's find the raw score x based on the z score z = -1<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "-1 = (x - 22.7)/(3.22)<BR>\n" );
document.write( "-1*3.22 = x - 22.7<BR>\n" );
document.write( "-3.22 = x - 22.7<BR>\n" );
document.write( "-3.22 + 22.7 = x<BR>\n" );
document.write( "19.48 = x<BR>\n" );
document.write( "x = 19.48<BR>\n" );
document.write( "x = 19.5\r<BR>\n" );
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document.write( "Answer: 19.5<BR>\n" );
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