document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113982>Question 1113982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let X be a normal random variable with zero mean and standard deviation u. Use the normal tables to compute the probabilities of the events { |X | &#8804;  k} and { |X| &#8805; k&#963;} for k = 1 , 2, 3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729009 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=729009\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> using the referenced normal distribution table, i get the following:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://users.stat.ufl.edu/~athienit/Tables/Ztable.pdf\" target = \"_blank\">referenced table</a>\r<BR>\n" );
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document.write( "area to the left of z-score of -1              =    .1587\r\n" );
document.write( "area to the left of z-score of  1              =    .8413\r\n" );
document.write( "area between z-score of -1 and z-score of 1    =    .6826 ***** 1\r\n" );
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document.write( "area to the left of z-score of -2              =    .0228\r\n" );
document.write( "area to the left of z-score of  2              =    .9772\r\n" );
document.write( "area between z-score of -2 and z-score of 2    =    .9544 ***** 2\r\n" );
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document.write( "area to the left of z-score of -3              =    .0013\r\n" );
document.write( "area to the left of z-score of  3              =    .9987\r\n" );
document.write( "area between z-score of -3 and z-score of 3    =    .9974 ***** 3\r\n" );
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document.write( "if you used the TI-84 Plus Calculator and rounded your answer to 4 decimal digits, you would get:\r\n" );
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document.write( "area between z-score of -1 and z-score of 1    =    .6827 ***** 1\r\n" );
document.write( "area between z-score of -2 and z-score of 2    =    .9545 ***** 2\r\n" );
document.write( "area between z-score of -3 and z-score of 3    =    .9973 ***** 3\r\n" );
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document.write( "as you can see, there are some slight differences due to rounding.\r<BR>\n" );
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document.write( "there is a calculator online that will show you graphically what the distribution curve looks like and the values you desire to find.\r<BR>\n" );
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document.write( "that calculator can be found at <a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>  \r<BR>\n" );
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document.write( "using that calculator, i get the following:\r<BR>\n" );
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document.write( "for z-score of -1 to 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/040501.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "for z-score of -2 to 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/040502.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "for z-score of -3 to 3:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/040503.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "using the table, there are a couple of ways to get the area in between.\r<BR>\n" );
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document.write( "the first is to get the area to the left the z-score of -x and then get the area to the left of the z-score of x and then subtracting the smaller area from the larger area to get the area in between.\r<BR>\n" );
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document.write( "since the table is symmetric about the mean, you can also just get the area to the left of the z-score of x and then subtract .5 from that and then double the result.\r<BR>\n" );
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document.write( "for example, z-score of 3 give you area to the left of it of .9987.<BR>\n" );
document.write( ".9987 - .5 = .4987<BR>\n" );
document.write( ".4987 * 2 = .9974\r<BR>\n" );
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document.write( "per the table used, this is accurate.\r<BR>\n" );
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document.write( "you could also take .9987 and subtract (1 - .9987) from it, to get .9987 - 1 + .9987 = .9974.\r<BR>\n" );
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document.write( "there are also different types of normal distribution tables in use.\r<BR>\n" );
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document.write( "there's the full table as reference above.\r<BR>\n" );
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document.write( "there is also the half table as referenced below: <a  rel=nofollow HREF= \"http://college.cengage.com/mathematics/brase/understanding_basic/3e/students/appendix/app_andm.pdf\" target = \"_blank\">normal distribution half table</a>\r<BR>\n" );
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document.write( "this table will tell you the area between the indicated positive z-score and a z-score of 0.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "area to the left of z-score of 3 = .4987.\r<BR>\n" );
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document.write( "if you want the area between a z-score of -3 and 3, you would simply double this to get .9974\r<BR>\n" );
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document.write( "if you want to get the full area to the left of the z-score of 3, you would add .5 to it to get .9987.\r<BR>\n" );
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document.write( "if you only wanted the area to the left of a z-score of -3, you would find the z-score of 3 to get .4987 and subtract it from .5 to get .0013.\r<BR>\n" );
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document.write( "the point being made is to make sure why type of normal distribution table you are dealing with.\r<BR>\n" );
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document.write( "most of the time it will be a full table, but sometimes you will see the half table.\r<BR>\n" );
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document.write( "if you use a calculator, you could ask the calculator to give you the area between a z-score of -x and x and the calculator will do all the arithmetic for you.\r<BR>\n" );
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document.write( "this is what i did using the TI-84 Plus, and using the online calculator referenced above.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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