document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137009>Question 1137009</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A distribution of values is normal with a mean of 148.3 and a standard deviation of 92.3.\r<BR>\n" );
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document.write( "Find the probability that a randomly selected value is less than -128.6. <BR>\n" );
document.write( "P(X < -128.6) = \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754868 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=754868\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean is 148.3 and the standard deviation is 92.3.\r<BR>\n" );
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document.write( "128.6 is equal to (148.3 - 128.6) / 92.3 = .2134344529 standard deviations below the mean.\r<BR>\n" );
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document.write( "since the mean in a z-score is 0 and the standard deviation in a z-score is equal to 1, then the z-score for 128.6 with a mean of 148.3 is equal to 0 - .2134344529 = -.2134344529.\r<BR>\n" );
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document.write( "you can confirm this using the z-score formula of z = (x - m) / s.\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation in this case.\r<BR>\n" );
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document.write( "you get z = (128.6 - 148.3) / 92.3 = -.2134344529.\r<BR>\n" );
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document.write( "if you use a z-score calculator to get the probability of getting a z-score less than -.2134344529, the calculator will tell you that the probability is equal to .4154940862.\r<BR>\n" );
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document.write( "that would be your solution if you were talking about a raw score of 128.6.\r<BR>\n" );
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document.write( "if you are talking about a raw score of minus 128.6, you would get a totally different answer.\r<BR>\n" );
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document.write( "in that case, z = (-128.6 - 148.3) / 92.3 gets you z = -3.\r<BR>\n" );
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document.write( "if you use a z-score calculator to get the probability of getting a z-score less than -3, the calculator will tell you that the probability is equal to <BR>\n" );
document.write( ".0013499672.\r<BR>\n" );
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document.write( "i used the normal distribution calculator in the TI-84 Plus to get these numbers.\r<BR>\n" );
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document.write( "there is an online calculator that will do the calculations for you and give you a visual display of the results.\r<BR>\n" );
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document.write( "it does round a bit more than the TI-84 Plus, but the answer will be reasonably close if you take the rounding into consideration.\r<BR>\n" );
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document.write( "that calculator can be found at <a  rel=nofollow HREF= \"\" target = \"_blank\"></a> and the results of the analysis are shown below.\r<BR>\n" );
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document.write( "the calculator can be used with z-score or it can be used with raw scores.\r<BR>\n" );
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document.write( "if used with z-scores, the mean is 0 and the standard deviation is 1.\r<BR>\n" );
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document.write( "if used with raw scores, the mean is the actual mean and the standard deviation is the actual standard deviation.\r<BR>\n" );
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document.write( "i used the area from a value part of the calculator and i did z-scores first and then raw scores to show you the difference and the fact that you get the same answer give or take a few due to possible rounding differences.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/032011.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/032012.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/032013.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/032014.jpg\" alt=\"$$$\" >\r<BR>\n" );
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