document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173518>Question 1173518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the z-score that corresponds to the following areas. <BR>\n" );
document.write( "Area to the left is 1.24<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798764 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=798764\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> with normal distributions, the total area is 1 and anything else has to be between 0 and 1.<BR>\n" );
document.write( "if we assume  you are talking in percents, then the total area is 100% and 1.24% / 100% would be equal to .0124.<BR>\n" );
document.write( "the z-score with an area of .0124 to the left of it would be equal to -2.244503871.<BR>\n" );
document.write( "round this to 3 decimal places and it becomes -2.245.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used my ti-84 plus scientific calculator to get the more detailed answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the tables and the calculators assume that the area is a ratio of the area to the left of the z-score divided by the whole area under the normal distribution curve.<BR>\n" );
document.write( "the whole area under the normal distribution curve is assumed to be equal to 1.<BR>\n" );
document.write( "that's why they show the area to the left of a z-score as a ratio between 0 and 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a reference on z-score tables and how to find the area to the left of the z-score.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://mathbitsnotebook.com/Algebra2/Statistics/STzScores.html#:~:text=To%20find%20a%20specific%20area,on%20a%20standard%20normal%20distribution.&text=You%20need%20both%20tables!\" target = _blank\">https://mathbitsnotebook.com/Algebra2/Statistics/STzScores.html#:~:text=To%20find%20a%20specific%20area,on%20a%20standard%20normal%20distribution.&text=You%20need%20both%20tables!</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "most tables are full tables, so concentrate on that.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the table i normally reference can be found at <a  rel=nofollow HREF= \"https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf\" target = \"_target =- \"_blank\">https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using that table, i found that the z-score of -2.24 gave an area of .01255 to the left of it and the z-score of -2.25 gave an area of .01222 to the left of it.<BR>\n" );
document.write( ".0124 was in between z-score of -2.24 and -2.25.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i manually interpolated to get a z-score of -2.2445 which is equal to -2.245 when rounded to 3 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "whether i used my ti-84 plus calculator, or used the table and manually interpolated,  i got a z-score of -2.245 rounded to 3 decimal places.<BR>\n" );
document.write( "that's usually close enough.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a calculator you can use online 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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using that calculator, i got a z-score of -2.245 with a lot less work than manual interpolation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );