document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182608>Question 1182608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Terri Vogel, an amateur motorcycle racer, averages per 129.95 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.28 seconds.<BR>\n" );
document.write( "The distribution of her race times is normally distributed.<BR>\n" );
document.write( "We are interested in one of her randomly selected laps.<BR>\n" );
document.write( "Let X be the number of seconds for a randomly selected lap.<BR>\n" );
document.write( "Round to 4 decimals.<BR>\n" );
document.write( "a. What is the distribution of X?<BR>\n" );
document.write( "   =129.95 over 2.28\r<BR>\n" );
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document.write( "b. Find the proportion of her laps that are completed between 126.17 and 127.91 seconds.\r<BR>\n" );
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document.write( "c. Find the fastest 4% of laps are under ______ seconds.\r<BR>\n" );
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document.write( "d. The middle 40% of her laps are from ______ seconds to _______ seconds.<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 #813766 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> X~N(129.95, 5.1984) units seconds, seconds^2 (use the variance)<BR>\n" );
document.write( "z=(x-mean)/sd<BR>\n" );
document.write( "z=-3.78/2.28=-1.658<BR>\n" );
document.write( "z=(-2.04/2.28)=-0.895<BR>\n" );
document.write( "that probability is 0.1367<BR>\n" );
document.write( "can check with 2ndVARS2(normalcdf(126.17,127.91,129.95,2.28)ENTER which is unrounded and 0.1368. I would use the first, unless the course requires no rounding of the z-value until the end.\r<BR>\n" );
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document.write( "The fastest 4% of laps: z(0.04), since want the shortest time, z=-1.7506<BR>\n" );
document.write( "-1.7506=(x-129.95)/2.28<BR>\n" );
document.write( "=125.96 seconds<BR>\n" );
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document.write( "This requires z (0.3) and z(0.7), which are -0.5244 and +0.5244 respectively<BR>\n" );
document.write( "-0.5244=(x-129.95)/2.28<BR>\n" );
document.write( "x=128.75 sec<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=131.15 sec<BR>\n" );
document.write( "If this is checked, it is about 0.4013 of the laps, the discrepancy's being that the multiplying z by -0.5244 gives 1.1956 seconds, which was rounded upward to 1.20 seconds. </SPAN>\n" );
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