document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197729>Question 1197729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The salaries of the employees of a corporation are normally distributed with a mean of $58,750 and a standard deviation of $4700.\r<BR>\n" );
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document.write( "A. What is the probability that a randomly selected employee will have a salary of at least $63,000?\r<BR>\n" );
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document.write( "B. What is the probability that a randomly selected employee will have a salary less that $50,000?\r<BR>\n" );
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document.write( "C. What are the minimum and maximum salaries of the middle 95% of the employees?\r<BR>\n" );
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document.write( "D. What would be the salary of an employee have to be to be in the top 5% of all employees? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831272 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=831272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 58,750.<BR>\n" );
document.write( "standard deviation = 4,700.<BR>\n" );
document.write( "z = (x - m) / s<BR>\n" );
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( "A. What is the probability that a randomly selected employee will have a salary of at least $63,000?\r<BR>\n" );
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document.write( "z = (63,000 - 58,750) / 4,700 = .9043 rounded to 4 decimal places.<BR>\n" );
document.write( "using the ti-84 plus, i find that the area to the right of that z-score = .1829 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "i confirmed with the online calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a> that this is correct.\r<BR>\n" );
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document.write( "B. What is the probability that a randomly selected employee will have a salary less that $50,000?\r<BR>\n" );
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document.write( "z = (50,000 - 58750) / 4700 = -1.8617 rounded to 4 decimal places.<BR>\n" );
document.write( "using the ti-84 plus, i find that the area to the left of that z-score = .0313 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "i confirmed with the online calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a> that this is correct.\r<BR>\n" );
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document.write( "C. What are the minimum and maximum salaries of the middle 95% of the employees?\r<BR>\n" );
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document.write( "middle 95% of employees would have z-score with .025 area to the left of it on the low side and .025 area to the right of it on the high side.<BR>\n" );
document.write( "using the ti-84 plus, i get the low side z-score equal to -1.9600 rounded to 4 decimal places, and i get the high side z-score equal to 1.9600 rounded to 4 decimal places.<BR>\n" );
document.write( "the area to the left of z-score of -1.9600 is equal to .025.<BR>\n" );
document.write( "the area to the left of z-score of 1.9600 is equal to .975.<BR>\n" );
document.write( "the area in between is equal to .975 minus .025 = .95.<BR>\n" );
document.write( "use the z-score formula to find the raw score.<BR>\n" );
document.write( "z = (x - m) / s becomes -1.9600 = (x - 58750) / 4700 on the left side of the interval.<BR>\n" );
document.write( "solve for x to get x = -1.9600 * 4700 + 58750 = 49538.<BR>\n" );
document.write( "z = (x - m) / s becomes 1.9600 = (x - 58750) / 4700 on the right side of the interval.<BR>\n" );
document.write( "solve for x to get x = 1.9600 * 4700 + 58750 = 67962.<BR>\n" );
document.write( "the middle 95% of the employees will make between 49538 and 67962 salary per year.\r<BR>\n" );
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document.write( "i confirmed with the online calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a> that this is correct.\r<BR>\n" );
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document.write( "D. What would be the salary of an employee have to be to be in the top 5% of all employees?\r<BR>\n" );
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document.write( "using the t-84 plus, i get the z-score that has .05 area to the right of it equal to 1449.<BR>\n" );
document.write( "the raw score will be based on the z-score formula as shown below:<BR>\n" );
document.write( "4.6449 = (x - 58750) / 4700.<BR>\n" );
document.write( "solve for x to get x = 1.6449 * 4700 + 58750 = 66481.03.\r<BR>\n" );
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document.write( "i confirmed with the online calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a> that this is correct.\r<BR>\n" );
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document.write( "here are the results from using the calculator.\r<BR>\n" );
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document.write( "using the online calculator, you can work directly with the raw scores instead of the z-scores.<BR>\n" );
document.write( "if you want to work with the z-scores, you enter a mean of 0 and a sandard deviation of 1.<BR>\n" );
document.write( "if y ou want to work with the raw scores, you enter the mean and the standad deviation required by the problem.\r<BR>\n" );
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document.write( "you can also get the z-scores and the areas using the z-score table, but the calculators make it easier and they are accurate to more decimal places.\r<BR>\n" );
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document.write( "if you need to know how to use the tables, let me know and i'll give you a tutorial on that.\r<BR>\n" );
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document.write( "theo </SPAN>\n" );
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