document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098608>Question 1098608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.0559 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713217 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=713217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you have a calculator that does statistics, like the texas instruments TI-84 plus, than you would take the inverse norm of .559 and the calculator would tell you that the z-score that has .559 area under the distribution curve to the left of it is .1484343318 which you would probably round to 2 decimal places and you would get .15\r<BR>\n" );
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document.write( "if you use a standard z-score table, you would look for an area to the left of a z-score that is closest to .559.\r<BR>\n" );
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document.write( "you would probably find that .5557 = .14 and .5596 = .15<BR>\n" );
document.write( "since .5596 is closer to .559 than .5557, you would go with z = .15\r<BR>\n" );
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document.write( "there are online calculator that would get you the inverse.\r<BR>\n" );
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document.write( "one such calculator can be found at <a  rel=nofollow HREF= \"http://stattrek.com/online-calculator/normal.aspx\" target = \"_blank\">http://stattrek.com/online-calculator/normal.aspx</a>\r<BR>\n" );
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document.write( "give it the area to the left of the z-score and it will tell you the z-score.\r<BR>\n" );
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document.write( "the table i used can be found at <a  rel=nofollow HREF= \"http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf\" target= \"_blanak\">http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf</a>\r<BR>\n" );
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document.write( "here's a picture of what i found.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/102410.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the areas to the left of the z-score are .5557 and .5596.\r<BR>\n" );
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document.write( "the row that they are on shows a z-score of .1<BR>\n" );
document.write( "the columns that they are on show z-scores of .04 and .05<BR>\n" );
document.write( "you add .1 to .04 and you get .14<BR>\n" );
document.write( "you add .1 to .05 and you get .15\r<BR>\n" );
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document.write( ".15 has the area to the left of the z-score that is closest to .559, therefore choose .15.\r<BR>\n" );
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document.write( "if you want better accuracy, you can interpolate manually or use a calculator.\r<BR>\n" );
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document.write( "most times rounding to the nearest 2 decimal digits on the z-score is good enough.\r<BR>\n" );
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document.write( "a manual interpolation is not quite as accurate as a calculator generated result, but it gets you closer than you would have been otherwise.\r<BR>\n" );
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document.write( "a manual interpolation of what this table shows would get you the following.\r<BR>\n" );
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document.write( ".5557 to .559 is equal to .0033<BR>\n" );
document.write( ".5557 to .5596 is equal to .0039<BR>\n" );
document.write( ".0033 / .0039 = .8461538462<BR>\n" );
document.write( ".14 to .15 = .01<BR>\n" );
document.write( ".8461538462 * .01 = .008415385<BR>\n" );
document.write( ".14 + .008415385 = .148415385 rounded to 3 decimal places = .148\r<BR>\n" );
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document.write( "your manual approximation would be .148 which is pretty close to what the calculator would have given you.\r<BR>\n" );
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document.write( "so, you would either go with .15 or with .148, depending on the accuracy required.\r<BR>\n" );
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document.write( "visually, your area to the left of the z-score of .148 would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/102411.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "this is through the use of another calculator by david m. lane that gets your results and gives you a visual of what it looks like.\r<BR>\n" );
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document.write( "that calculator can be found 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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