document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203452>Question 1203452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A study of furniture wholesales,inc regarding the payment of invoice revealed that, on the average, an invoice was paid 20 days after it was received. The standard deviation equaled 5 days. What is the probability of selecting invoice and finding it was paid between 18 and 26 days after it was paid  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839028 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=839028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use of the calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = _blank\">https://davidmlane.com/hyperstat/z_table.html</a> can help answer this.\r<BR>\n" );
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document.write( "the resullt shows that the probability of getting an invoice paid between 18 and 26 days is equal to .5404.\r<BR>\n" );
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document.write( "if you want to solve this using z-scores, you would do the following.\r<BR>\n" );
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document.write( "z = (x-m)/s formula is used.<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the desired value<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( "on the low side, the formula becomes z = (18 - 20) / 5 = -.4.\r<BR>\n" );
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document.write( "on the high side, the formula becomes z = (26 - 20) / 5 = 1.2\r<BR>\n" );
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document.write( "using the same calculaator, you would make the mean = 0 and the standard deviation = 1 and you would get probability of getting a z-score between -.2 and 1.2 = .5404.\r<BR>\n" );
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document.write( "you could also have solved it by doing the following:\r<BR>\n" );
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document.write( "low z-score = -.4<BR>\n" );
document.write( "area to the left of that = .3446<BR>\n" );
document.write( "high z-score = 1.2<BR>\n" );
document.write( "area to the left of that = .8849<BR>\n" );
document.write( "area in between = .5403.\r<BR>\n" );
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document.write( "this method could be used with the calculaator, as we just did, or it could be used with the z-score tables that provide the area to the left of the z-scores.\r<BR>\n" );
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document.write( "such a table can be found at <a  rel=nofollow HREF= \"https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf\" target = \"_blank\">https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf</a>\r<BR>\n" );
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document.write( "using that table, you would find that the area to the left of a z-score of:<BR>\n" );
document.write( "-.4 = .34458<BR>\n" );
document.write( "2.2 = .88493<BR>\n" );
document.write( "area in between would be equal to the larger area minus the smaller area = .54035.\r<BR>\n" );
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document.write( "with the calculator, you can get the answer directly from the mean and the standad deviation or with the z-score.<BR>\n" );
document.write( "with the z-score, the mean is always 0 and the standad deviatioon is always 1.\r<BR>\n" );
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document.write( "with the table, you have to use the z-score.\r<BR>\n" );
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document.write( "here are the results using the calculator directly from the raw score, mean and standard deviation.\r<BR>\n" );
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document.write( "here are the results using the calculator from the z-score.  with this method, the mean is always 0 and the standard deviation is always 1.\r<BR>\n" );
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document.write( "the calculator can get you the area in between directly, whether you use the raw score method or the z-score method.\r<BR>\n" );
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document.write( "with the table, you can only use the z-score and the subtraction of area to the left of the low z-score from the areaa to the left of the high z-score method.\r<BR>\n" );
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document.write( "here are the results using the calculator with the subtraction method.<BR>\n" );
document.write( "this mimics what you would get using the table.\r<BR>\n" );
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