document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186247>Question 1186247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a standard normal distribution, find:\r<BR>\n" );
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document.write( "P(-2.81 < z < -1.24) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817135 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=817135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can find the area to the left of -2.81 and the area to the left of -1.24.<BR>\n" );
document.write( "you would then subtract the smaller area from the larger area.<BR>\n" );
document.write( "the remainder is the area between those two z-scores.\r<BR>\n" );
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document.write( "alternatively, you can find the area in between directly, depending on the capabilities of the normal distribution calculator that you use.\r<BR>\n" );
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document.write( "you can also do it using a z-score table that tells you the area to the left of the z-score.\r<BR>\n" );
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document.write( "using the z-score table 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>, i get the following.\r<BR>\n" );
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document.write( "area to the left of -2.81 = .00248.<BR>\n" );
document.write( "area to the left of -1.24 = .10749.\r<BR>\n" );
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document.write( "the units and tens digit of the z-score is on the left in the first column.<BR>\n" );
document.write( "the hundreds digit is on that row with the first column to the right = .00, then up each digit until .09.\r<BR>\n" );
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document.write( "for example, -1.24 shows -1.2 on the first column and then .04 on the fifth column of that row.<BR>\n" );
document.write( "together they make  -1.24 because -1.2 + .04 = -1.24.\r<BR>\n" );
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document.write( "if you look at the column heading on the top of each page, you'll see that's what it shows in the firth column, i.e. .04\r<BR>\n" );
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document.write( "here's a display, broken down to show you the heading of the columns and the particular rows of interest.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/101701c.jpg\" >\r<BR>\n" );
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document.write( "here's what the table looked like before i cut it up.\r<BR>\n" );
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document.write( "subtract smaller area from larger area to get area in between = .10501.\r<BR>\n" );
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document.write( "my ti-84 plus tells me that the area in between is .1050106258 = .10501 rounded to 5 decimal digits.\r<BR>\n" );
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document.write( "using the calculator at <a  rel=nofollow HREF= \"https://www.statskingdom.com/normal.html\" target = \"_blank\">https://www.statskingdom.com/normal.html</a>, i get:\r<BR>\n" );
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document.write( "area in between = .10501 when rounded to 5 decimal laces.\r<BR>\n" );
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document.write( "here's a display from that calculator.\r<BR>\n" );
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document.write( "using the same calculator, and only looking for the area to the left of the z-score, i get:\r<BR>\n" );
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document.write( "area to the left of -1.24 = .10748800<BR>\n" );
document.write( "area to the left of -2.81 = .00247707\r<BR>\n" );
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document.write( "here are the displays from that calculator.\r<BR>\n" );
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document.write( "you're looking for the second entry under the calculate button.\r<BR>\n" );
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document.write( "area in between is smaller area subtracted from larger area = .10105093 = .10501 when rounded to 5 decimal digits.\r<BR>\n" );
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document.write( "here are the displays from that calculator.\r<BR>\n" );
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