document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074409>Question 1074409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I hope this is in the right category. \r<BR>\n" );
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document.write( "The monthly salaries in a company with 5000 employees are normally distributed. The mean salary is $3100 with a standard deviation of $700. What percentage of employees earn more than $2400 per month? How many employees earn more than $2400 per month? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689107 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=689107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 3100<BR>\n" );
document.write( "standard deviation is 700.\r<BR>\n" );
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document.write( "2400 is (3100 - 2400) / 700 = 1 standard deviation from the mean in a negative direction.\r<BR>\n" );
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document.write( "that makes the z-score equal to -1.\r<BR>\n" );
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document.write( "with z-scores, the mean is 0 and the z-score is the number of standard deviations away from the mean.\r<BR>\n" );
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document.write( "the formula is z = (x-m) / s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the  mean <BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "the formula becomes z = (2400 - 3100)/700 = -700/700 = -1\r<BR>\n" );
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document.write( "to find the percentage of employees that earn more than a z-score of -1, look up in the z-score table for a rate (rate = % / 100) to the left of a z-score of -1.\r<BR>\n" );
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document.write( "then take 1 minus that rate for a rate to the right of a z-score of -1.\r<BR>\n" );
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document.write( "if you used the table linked to below, you would have found the rate to the left of the z-score of -1 equal to .1587 and then gotten the rate to the right of the z-score of -1 equal to 1 - .1587 = .8413.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf\" target = \"_blank\">http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf</a>\r<BR>\n" );
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document.write( "alternatively use a calculator that goes normal distribution type problems.\r<BR>\n" );
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document.write( "i used the following calculator.\r<BR>\n" );
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document.write( "<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( "if allows me to find the rate to the left of or to the right of a particular z-score or in between 2 z-scores or outsides of 2 z-scores.\r<BR>\n" );
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document.write( "very nice calculator.\r<BR>\n" );
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document.write( "i got a rate of .8413\r<BR>\n" );
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document.write( "that means that 84.13% of the employees earn more than 2400 per month.\r<BR>\n" );
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document.write( "the number of employees that earn more than 2400 per month would be equal to 5000 * .8413 = 4206.5 which would be rounded to 4206 or 4207.\r<BR>\n" );
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document.write( "by convention of mathematical rounding rules, you would round to 4207.\r<BR>\n" );
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document.write( "the same calculator can be used with raw scores or z-scores.\r<BR>\n" );
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document.write( "with z-scores, mean is 0 and standard deviation is 1.\r<BR>\n" );
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document.write( "with raw scores, mean is 3100 and standard deviation is 700.\r<BR>\n" );
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document.write( "results are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/032701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/032702.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the same calculator can be used to find the area from the z-score or the z-score from the area.\r<BR>\n" );
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document.write( "it can do the same using the raw mean score and standard deviation as well.\r<BR>\n" );
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document.write( "nice calculator.\r<BR>\n" );
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document.write( "even gives you a picture of the area under the distribution curve that it calculated for you.\r<BR>\n" );
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document.write( "use of the table rather than the calculator would have given you a result as shown below.\r<BR>\n" );
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document.write( "it's more work, but you get the same answer if you do it right.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/032703.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src =\"http://theo.x10hosting.com/2017/032705.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the row heading would -1.0 and the column heading would be .00\r<BR>\n" );
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document.write( "add them together and you get a z-score of -1.00.<BR>\n" );
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