document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261478>Question 261478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help?<BR>\n" );
document.write( "2.  The mean amount of time a (unnamed) computer server is down is 18.3 minutes with a standard deviation of 5.7 minutes.  \r<BR>\n" );
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document.write( "a.  Assuming we know nothing about the shape of the data set, at least what percentage of times will the server be down between 8.325 and 28.275 minutes?  <BR>\n" );
document.write( "b.  Assuming we can verify that the data set is approximately normally distributed, what percentage of times will the server be down less than 24 minutes?  <BR>\n" );
document.write( "c.  Assuming we can  verify that the data set is approximately normally distributed, 68% of the server downtimes will be within what range?  (5 points)\r<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 #192807 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=192807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The mean amount of time a (unnamed) computer server is down is 18.3 minutes with a standard deviation of 5.7 minutes. <BR>\n" );
document.write( "a. Assuming we know nothing about the shape of the data set, at least what percentage of times will the server be down between 8.325 and 28.275 minutes?<BR>\n" );
document.write( "Find a z-score for each of those numbers:<BR>\n" );
document.write( "z(8.325) = (8.325-18.3)/5.7 = -1.75<BR>\n" );
document.write( "z(28.275) = (28.275-18.3)/5.7 = 1.75<BR>\n" );
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document.write( "According to Chebeshev at least (1-(1/1.75^2))% of the data lies<BR>\n" );
document.write( "between those numbers.<BR>\n" );
document.write( "Ans: (1-(1/1.75)^2) = 0.6734 = 67.34%<BR>\n" );
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document.write( "b. Assuming we can verify that the data set is approximately normally distributed, what percentage of times will the server be down less than 24 minutes?<BR>\n" );
document.write( "z(24) = (24-18.3)/5.7 = 1<BR>\n" );
document.write( "P(x<24)=P(z<1) = 0.8413 = 84.13% of the time<BR>\n" );
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document.write( "c. Assuming we can verify that the data set is approximately normally distributed, 68% of the server downtimes will be within what range? <BR>\n" );
document.write( "68% of the population is within 1 std of the mean<BR>\n" );
document.write( "Ans: 18.3 - 5.7 < x < 18.3 + 5.7<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " \r<BR>\n" );
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