document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028318>Question 1028318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4.	Suppose that a school district wants to start a program for gifted students.  The participants in the program are to be chosen on the basis of IQ scores (normal with &#61549; = 100, &#61555; = 15).  If the school district wants only the top 2% of students to participate in the program, what should be the IQ score that students must exceed to be accepted? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643479 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=643479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> from what i understand:\r<BR>\n" );
document.write( "\n" );
document.write( "mean is 100<BR>\n" );
document.write( "standard deviation is 15.<BR>\n" );
document.write( "you want the iq score that represents the top 2%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "look up in z-score table for area under the distribution curve of .98.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that would be the area to the left of the z-score in most z-score tables that are full tables, meaning they show z-scores of roughly -3.5 to + 3.5 or thereabouts.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you have a half table that only shows z-scores from 0 to + 3.5 or thereabouts, then you need to translate differently.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i'll assume you  have a full table.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you have a half table, then let me know and i'll change the procedure to accommodate that.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assuming the full table, .....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "an area to the left of the z-score of .98 means the area to the right of that z-score is 1 - .98 = .02\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that equates to the student being in the top 2%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the table i used has the closest area above .98 to be .9803 and the closest area below .98 to be .9798.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".9798 give you a z-score of 2.05<BR>\n" );
document.write( ".9803 give you a z-score of 2.06\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".98 will be somewhere between there, probably somewhere around 2.053 or 2.054.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i confirmed, using my calculator, that an area of .98 to the left of the indicated z-score will lead to a z-score of 2.0537.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now to translate that z-score to a raw score.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your mean is 100<BR>\n" );
document.write( "your standard deviation is 15.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "formula for z-score is z = (x-m)/s\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x is the raw score you are looking for.<BR>\n" );
document.write( "m is the mean of 100<BR>\n" );
document.write( "s is the standard deviation of 15<BR>\n" );
document.write( "z is the z-score which you know to be 2.0537\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "formula becomes 2.0537 = (x - 100) / 15\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = 15 * 2.0537 + 100 = 130.8055.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "an iq of 130.8055 or above would qualify as being in the top 2%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this answer might be more exact than you would get using your table.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "more than likely your table led you to a z-score of 2.05 or 2.06.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a z-score of 2.05 would lead to a raw score of 15 * 2.05 + 100 = 130.75\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a z-score of 2.06 would lead to a raw score of 15 * 2.06 + 100 = 130.9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a z-score of 2.06 means that students with that z-score would be in the top 1 - .9803 = .0197 or 1.97% of their class.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a z-score of 2.05 means that students with that z-score would be in the top 1 - .9798 = .0202 or 2.02% of their class.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "either one would be close, but to ensure that you were in the top 2% or less of the class, the z-score of 2.06 would be preferable.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "not knowing exactly what your instructors are looking for, this is the best that i can do.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you need further clarification, or can provide more details about what you need, then send me an email and i'll try to improve on the answer accordingly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );