document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134998>Question 1134998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let z denote a variable that has a standard normal distribution. Determine the value z* to satisfy the following conditions. (Round all answers to two decimal places.)\r<BR>\n" );
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document.write( "P(z > z* or z < −z*) = 0.1974  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752525 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=752525\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in order for the probability of z being greater than z*, the area to the right of z* must be equal to .1974.\r<BR>\n" );
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document.write( "in order for the probability of z being less than -z*, the area to the left of z* must be equal to .1974\r<BR>\n" );
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document.write( "so you're looking for a z* that has an area to the right of it of .1974 and you're looking for a -z* that has an area to the left of it of .1974.\r<BR>\n" );
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document.write( "since the normal distribution is symmetric about the mean, z* and -z* have the same absolute value.\r<BR>\n" );
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document.write( "you can use a normal distribution calculator to get the answer for you or you can manually try to derive the answer using the z-score table.\r<BR>\n" );
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document.write( "the use of a calculator is recommended.\r<BR>\n" );
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document.write( "one such 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( "this calculator works similar to the way you would use the normal distribution tables in that it gives you the area to the left of the indicated z-score.\r<BR>\n" );
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document.write( "in my first use of this calculator, i gave it a cumulative probability of .1974 and it told me that the z-score with an area under the normal distribution curve of .1974 to the left of it was -.851.\r<BR>\n" );
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document.write( "here is a display of the result.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021801a.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "to find the area of .1974 to the right of the z-score, i had to generate the area to the left of the z-score.\r<BR>\n" );
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document.write( "if the area to the right of the z-score is .1974, then the area to the left of the z-score is equal to 1 - .1974 = .8026.\r<BR>\n" );
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document.write( "since this calculator only gives you the area to the left of the z-score, then in my second use of this calculator, i gave it a cumulative probability of .8026 and it told me that the z-score with an area under the normal distribution curve of .8026 to the left of it was .851.\r<BR>\n" );
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document.write( "here is a display of the result.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021802a.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "i now have a z-score with an area of .1974 to the left of it equal to -.851 and a z-score with an area of .1974 to the right of it equal to .851.\r<BR>\n" );
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document.write( "since the normal distribution curve is symmetric about the mean, this is the result i expected to see.\r<BR>\n" );
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document.write( "this is also the answer to your problem.\r<BR>\n" );
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document.write( "z* is equal to .851<BR>\n" );
document.write( "-z* is equal to -.851\r<BR>\n" );
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document.write( "while the calculator shown above can be used and it is similar to the procedure you would use to manually find the z-score, there is another online calculator that is much more useful and visually attractive.\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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document.write( "using this calculator, i was able to find the answer directly by asking the calculator to give me the z-score with the area of .1974 to the left of it and by asking it to give me the z-score with  the area of .1975 to the right of it.\r<BR>\n" );
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document.write( "here's the result of asking it to find me the z-score with an area of .1974 to the left of it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021803.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "here's the result of asking it to find me the z-score with an area of .1974 to the right of it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021804.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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