document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151683>Question 1151683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to solve this question:<BR>\n" );
document.write( "Assume that the random variable X is normally distributed, with mean=31.5 and standard deviation=1.4. Compute the probability P(X<28). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773571 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=773571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are online calculators that allow you to solve this directly without  having to figure out what the z-score is.<BR>\n" );
document.write( "one such calculator can be found at <a  rel=nofollow HREF= \"https://www.omnicalculator.com/statistics/normal-distribution\" target = \"_blank\">https://www.omnicalculator.com/statistics/normal-distribution</a><BR>\n" );
document.write( "i used this calculator and input a mean of 31.5 and a standard deviation of 1.4 and an X value of 28.<BR>\n" );
document.write( "the calculator gave me p(X < 28), shown as p(x < X).<BR>\n" );
document.write( "it also gave me p(X > 28), shown as p(x > X).<BR>\n" );
document.write( "it also gave me the z-score, shown as -2.5.<BR>\n" );
document.write( "here's what the output looked like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/012811.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "i also used another normal distribution calculator that gives you the result and also shows you a visualization of that looks like under the normal distribution curve.\r<BR>\n" );
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document.write( "that calculator can be found at <a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "with this calculator, you can enter z-score of -2.5 with a mean of 0 and a standard deviation of 1, or you can enter a raw score of 28 with a mean of 31.5 and a standard deviation of 1.4\r<BR>\n" );
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document.write( "here's what the results from that calculator look like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/012812.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/012813.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "note that the probability of getting a score < 28 using this calculator was slightly different than the probability using the omni calculator.<BR>\n" );
document.write( "this will happen when using different calculator because they may not all have the same underlying assumptions regarding interpolation of results between known value and / or different assumption regarding intermediate rounding of results.<BR>\n" );
document.write( "for practical purposes, probability estimates rounded from 2 to 4 decimal places should be all that you need.\r<BR>\n" );
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document.write( "the omni calculator will give you the z-score if you give it the mean of 31.5 and an X value of 28 and a standard deviation of 1.4\r<BR>\n" );
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document.write( "the david m. lane calculator will give you the result if you give it the mean of 31.5 and an X value of 28 and a standard deviation of 1.4, but it won't give you the z-score.\r<BR>\n" );
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document.write( "to find the z-score, you would need to use the z-score formula.<BR>\n" );
document.write( "that formula is z = (x - m) / s<BR>\n" );
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.<BR>\n" );
document.write( "using that formula, you would get:<BR>\n" );
document.write( "z = (28 - 31.5) / 1.4<BR>\n" );
document.write( "solve for z to get z = -2.5\r<BR>\n" );
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document.write( "the omni calculator give me the same result that i get from using my TI-84 Plus calculator, with less effort.<BR>\n" );
document.write( "bottom line:<BR>\n" );
document.write( "omni is pretty good.<BR>\n" );
document.write( "there is also an advance mode that can give you the probability between two values, either from 2 z-scores or from 2 raw scores.\r<BR>\n" );
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document.write( "for your purposes, p(x < X) where X = 28 would be .0062 rounded to 4 decimal places.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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