document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136419>Question 1136419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a recent year, the ACT scores for high school students with an A or B grade point average were normally distributed with a mean of 24.2 and a standard deviation of 4.2. A student with an A or B average who took the ACT during this time is selected.\r<BR>\n" );
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document.write( "Find the probability that a student’s ACT score is less than 21 or more than 33.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754464 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=754464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 24.2 and standard deviation is 4.2.\r<BR>\n" );
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document.write( "you can use the following calculator to answer this question.\r<BR>\n" );
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document.write( "<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( "your solution will be:\r<BR>\n" );
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document.write( "probability that a score is less than 21 is equal to .2231.\r<BR>\n" );
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document.write( "the results are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/031401.JPG\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "probability that a score is greater than 33 is equal to .0181.\r<BR>\n" );
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document.write( "the results are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src =\"http://theo.x10hosting.com/2019/031402.JPG\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "if you wanted to solve this using z-scores, you would do the following:\r<BR>\n" );
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document.write( "the formula for z-score is 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.\r<BR>\n" );
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document.write( "m is 24.2<BR>\n" );
document.write( "s is 4.2\r<BR>\n" );
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document.write( "when x = 21, the z-score is (21 - 24.2) / 4.2 = -.7619048\r<BR>\n" );
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document.write( "when x = 33, the z-score is (33 - 24.2) / 4.2 = 2.095238095.\r<BR>\n" );
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document.write( "you would use the same calculator, only you would set the mean to 0 and the standard deviation to 1.\r<BR>\n" );
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document.write( "you would get the same answers as before, only this time you are suing the z-score rather than the raw score.\r<BR>\n" );
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document.write( "here's the results.\r<BR>\n" );
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document.write( "for less than -.761905.\r<BR>\n" );
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document.write( "for greater than 2.095238.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/031404.JPG\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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