document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142646>Question 1142646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the z-score boundaries that separate a normal distribution as described in each of the following.  \r<BR>\n" );
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document.write( "The middle 30% from the 70% in the tails.\r<BR>\n" );
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document.write( "The middle 42% from the 58% in the tails. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763352 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=763352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if 70% is in the tails, then half of that is in the left tail and half of that is in the right tail.\r<BR>\n" );
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document.write( "if you find the z-score for the left tail, then the same z-score with the opposite sign will be the z-score for the right tail.\r<BR>\n" );
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document.write( "specifically.\r<BR>\n" );
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document.write( "30% is in the middle which means 70% / 2 = 35% is in the left tail.\r<BR>\n" );
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document.write( "you look for a z-score that has .35 of the area under the normal distribution curve to the left of it.\r<BR>\n" );
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document.write( "that z-score will be -.385 rounded to 3 decimal places.\r<BR>\n" );
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document.write( "that will be the low z-score.<BR>\n" );
document.write( "the high z-score will be +.385 rounded to 3 decimal places.\r<BR>\n" );
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document.write( "you can use the online z-score calculator 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( "you would use the value from an area portion of this calculator and you would look for the z-score that has .30 area between.\r<BR>\n" );
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document.write( "the calculator will then tell you the lower and upper z-score bounds for that area.\r<BR>\n" );
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document.write( "a display of the results are shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/062705.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "you would do a similar analysis for the middle 42%.\r<BR>\n" );
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document.write( "58% in the tails divided by 2 = 29% in the left tail and 29% in the right tail.\r<BR>\n" );
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document.write( "the z-score with an area of .29 under the normal distribution curve to the left of it would be a z-score of -.553 rounded to 3 decimal places.\r<BR>\n" );
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document.write( "the low z-score is -.553<BR>\n" );
document.write( "the high z-score is +.553\r<BR>\n" );
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document.write( "using the same online z-score calculator, the display of the results are shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/062706.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "i used the inverse norm function of the TI-84 Plus to find the z-score from the area.\r<BR>\n" );
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document.write( "if you need help understanding how to do that by using the normal distribution tables, let me know and i'll take you through it.\r<BR>\n" );
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document.write( "use of a calculator is far easier and more accurate.\r<BR>\n" );
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document.write( "one such online calculator can be found at <a  rel=nofollow HREF= \"https://stattrek.com/online-calculator/normal.aspx\" target = \"_blank\">https://stattrek.com/online-calculator/normal.aspx</a>\r<BR>\n" );
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document.write( "give it a try.\r<BR>\n" );
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document.write( "if you can't find the left hand z-score using this calculator, let me know and i'll take you through it.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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