document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206701>Question 1206701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1092 and a standard deviation of 197. Scores on the ACT test are normally distributed with a mean of 21.6 and a standard deviation of 4.4. It is assumed that the two tests measure the same aptitude, but use different scales. Round all answers to 1 decimal place.\r<BR>\n" );
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document.write( "If a student gets an SAT score that is the 49-percentile, find the actual SAT score. SAT score =\r<BR>\n" );
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document.write( "What would be the equivalent ACT score for the student?ACT score=\r<BR>\n" );
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document.write( "If a student gets an SAT score of 1367.8, find the equivalent ACT score. ACT score= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844305 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=844305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you would use the z-scores to make these measurements comparable between the two normal distributions.\r<BR>\n" );
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document.write( "the SAT mean is 1092 and standard deviation is 197.\r<BR>\n" );
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document.write( "the ACT mean is 21.6 and the standard deviation is 4.4.\r<BR>\n" );
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document.write( "the 49th percentile means that 49% of all scores are below that.<BR>\n" );
document.write( "under the normal distribution curve, that would be the area to the left of the equivalent z-score.\r<BR>\n" );
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document.write( "you would use the z-score table or a z-score calculator to find the z-score associated with an area of .49 to the left of it.\r<BR>\n" );
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document.write( "the calculator that i used can be found at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "the calculator is set to getting a z-score with an area to the left of it equal to .49.\r<BR>\n" );
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document.write( "the results of that is shown below.\r<BR>\n" );
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document.write( "ddddd\r<BR>\n" );
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document.write( "the calculator says that the z-score is -.025.\r<BR>\n" );
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document.write( "you can use the z-score formula to find the equivalent raw scores for both the SAT scores and the ACT scores.\r<BR>\n" );
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document.write( "the z-score 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.\r<BR>\n" );
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document.write( "for the SAT, you get z = (x - m) / s becomes -.025 = (x - 1092) / 197.<BR>\n" );
document.write( "solve for x to get x = -.025 * 197 + 1092 = 1087.075.\r<BR>\n" );
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document.write( "for the ACT, you get z = (x - m) / s becomes -.025 = (x - 21.6) / 4.4.<BR>\n" );
document.write( "solve for x to get x = -.025 * 4.4 + 21.6 = 21.49.\r<BR>\n" );
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document.write( "the z-score for a SAT score of 1367.8 is found by solving the z-score formula of z = (x - m) / s becoming z = (1367.8 - 1092) / 197 = 1.4.\r<BR>\n" );
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document.write( "that z-score formula is used to find the comparable ACT score.\r<BR>\n" );
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document.write( "z = (x - m) / s becomes 1.4 = (x - 21.6) / 4.4.<BR>\n" );
document.write( "solve for x to get x = 1.4 * 4.4 + 21.6 = 27.76.\r<BR>\n" );
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document.write( "answers to your questions are:\r<BR>\n" );
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document.write( "If a student gets an SAT score that is the 49-percentile, find the actual SAT score.\r<BR>\n" );
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document.write( "the SAT score is 1087.1.\r<BR>\n" );
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document.write( "What would be the equivalent ACT score for the student?\r<BR>\n" );
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document.write( "the equivalent ACT score is 21.5.\r<BR>\n" );
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document.write( "If a student gets an SAT score of 1367.8, find the equivalent ACT score.\r<BR>\n" );
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document.write( "the equivalent ACT  score is 27.8.\r<BR>\n" );
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document.write( "the calculator at <a  rel=nofollow HREF= \"\" target = \"_blank\"></a> was used to calculate the z-scores.\r<BR>\n" );
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document.write( "it can also be used to calculate the raw scores directly.\r<BR>\n" );
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document.write( "with z-score, you set the mean and standard deviation to 0 and 1 resprecively.<BR>\n" );
document.write( "with raw scores, you set the mean and standard deviation to what they are.\r<BR>\n" );
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document.write( "the z-score analysis results are shown below:\r<BR>\n" );
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document.write( "the comparable raw score results are shown below.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo </SPAN>\n" );
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