document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134637>Question 1134637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose Z is a standard normal random variable.\r<BR>\n" );
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document.write( "1. If P(-z < Z < z) = 0.5098, find z.\r<BR>\n" );
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document.write( "2. Find P(-2.11 < Z < -0.37). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752104 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=752104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. If P(-z < Z < z) = 0.5098, find z.\r<BR>\n" );
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document.write( "the area between -z and z is equal to .5098.\r<BR>\n" );
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document.write( "the z-score in the middle between -z and z is equal to 0.\r<BR>\n" );
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document.write( "the area to the left of a z-score of 0 is equal to .5.\r<BR>\n" );
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document.write( "the area between -z and 0 is half the area between 0 and z.\r<BR>\n" );
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document.write( "because the normal distribution is symmetric, take .5098 and divide it by 2 to get .2549.\r<BR>\n" );
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document.write( "the area to the left of 0 is equal to .5\r<BR>\n" );
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document.write( "the between -z and 0 is equal to .2549.\r<BR>\n" );
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document.write( "subtract .2549 from .5 to get .2451.\r<BR>\n" );
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document.write( "that's the area to the left of -z.\r<BR>\n" );
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document.write( "solve for -z to get -z = -.6899907576.\r<BR>\n" );
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document.write( "that makes z = .699907576.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "the area between -.6899907576 and .699907576 is equal to .5098001472 which is equal to .5098 when rounded to 4 decimal digits.\r<BR>\n" );
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document.write( "the solution is confirmed to be good.\r<BR>\n" );
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document.write( "visually it looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021207.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "2. Find P(-2.11 < Z < -0.37).\r<BR>\n" );
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document.write( "the area between -2.11 and -.37 is equal to .3382621848\r<BR>\n" );
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document.write( "i think that's what you're looking for.\r<BR>\n" );
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document.write( "if it isn't, let me know what it is that you're looking for here.\r<BR>\n" );
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document.write( "here's a visual display of what i think you are looking for.\r<BR>\n" );
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document.write( "you look up the area to the left of a z-score of -2.11 and you look up the area to the left of a z-score of -.37 and you subtract the smaller area from the larger area to get your anser.\r<BR>\n" );
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document.write( "using my calculator, i got the following:\r<BR>\n" );
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document.write( "area to the left of a z-score of -2.11 is equal to .0174291159\r<BR>\n" );
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document.write( "area to the left of a z-score of -.37 is equal to .3556913007\r<BR>\n" );
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document.write( "after between -2.11 and -.37 is equal to .3556913007 minus .0174291159 which is equal to .3382621848.\r<BR>\n" );
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document.write( "that's the same as i got before when i asked the calculator for the area between a z-score of -2.11 and -.37 directly.\r<BR>\n" );
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document.write( "the calculator i use is the TI-84 Plus to solve problems like these.\r<BR>\n" );
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document.write( "here's a visual display.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021206.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "let meknow if you have any questions or need further clarification on points you don't understand.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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