document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=357731>Question 357731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> As reported in Runner’s World magazine, the times of the finishers in the New York City 10K Run are normally distributed with a mean of 61.2 minutes and a standard deviation of 9.3 minutes.  \r<BR>\n" );
document.write( "\n" );
document.write( "	a.	A runner is selected at random.  Find the probability that the runner’s finishing time was more than 75 minutes.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "	b.	A runner is selected at random.  Find the probability that the runner’s finishing time was between 60 and 63 minutes\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "	c.	Runners whose finishing times are in the top 5% are automatically invited to participate in next year’s race.  What finishing time separates the top 5% from the others? Round answer to 1 decimal place.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #255367 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=255367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As reported in Runner’s World magazine, the times of the finishers in the New York City 10K Run are normally distributed with a mean of 61.2 minutes and a standard deviation of 9.3 minutes.<BR>\n" );
document.write( "-------<BR>\n" );
document.write( " <BR>\n" );
document.write( "a. A runner is selected at random. Find the probability that the runner’s finishing time was more than 75 minutes. <BR>\n" );
document.write( "z(75) = (75-61.2)/9.3 = 1.4839<BR>\n" );
document.write( "----<BR>\n" );
document.write( "P(x > 75) = P(z > 1.4839) = normalcdf(1.4839,100) = 0.0689<BR>\n" );
document.write( "-------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "b. A runner is selected at random. Find the probability that the runner’s finishing time was between 60 and 63 minutes<BR>\n" );
document.write( "Find the z-value of 60 and of 63.<BR>\n" );
document.write( "Find the probability that z is between those z-values.<BR>\n" );
document.write( "------------------------------------------------------------- \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c. Runners whose finishing times are in the top 5% are automatically invited to participate in next year’s race. What finishing time separates the top 5% from the others? Round answer to 1 decimal place.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "find the z-value with a left tail of 5%.<BR>\n" );
document.write( "invNorm(0.95) = -1.645<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Find the x-value coressponding to that z-value:<BR>\n" );
document.write( "x = zs + u<BR>\n" );
document.write( "x = -1.645*9.3+61.2 = 45.90 seconds<BR>\n" );
document.write( "===============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );