document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173215>Question 1173215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a Statistics examination, the average score was 80 and the variance was 9. Students with scores ranging from 83 to 88 received a grade of 1.50. If the scores are approximately normally distributed and 11 students received a grade of 1.50, determine the percentage of students with scores lower than 83.<BR>\n" );
document.write( "Let X be the scores in Statistics exam. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798396 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=798396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 80<BR>\n" );
document.write( "standard deviation = square root of variance = sqrt(9) = 3\r<BR>\n" );
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document.write( "z-score is found by the following formula:<BR>\n" );
document.write( "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( "when x = 83, z = (83 - 80) / 3 = 3 / 3 = 1<BR>\n" );
document.write( "when x = 88, z = (88 - 80) / 3 = 8 / 3 = 8/3<BR>\n" );
document.write( "area to the left of a z-score of 1 is equal to .841345<BR>\n" );
document.write( "area to the left of a z-score of 8/3 is equal to .996170<BR>\n" );
document.write( "area in between 83 and 88 is equal to .996170 - .841345 = .154825\r<BR>\n" );
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document.write( "11 students had grades between 83 and 88.<BR>\n" );
document.write( "11/.154825 = approximately 71 students in total. <BR>\n" );
document.write( ".841345 * 71 = approximately 60 students who got grades less than 83.<BR>\n" );
document.write( "the balance of the students got grades greater than 88 = 1 - .84345 - .154825 = .00382 * 71 = less than 1.<BR>\n" );
document.write( "rounded that becomes 0.\r<BR>\n" );
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document.write( "the numbers don't really come out very well because they are not whole numbers and the percentages, especially of the scores above 88, don't relate very well to a whole number.<BR>\n" );
document.write( "in fact, a percentage that low would lead to a whole number of 0.\r<BR>\n" );
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document.write( "to answer the question, i think all you had to do was find the area under the normal distribution curve to the left of a score of 83.<BR>\n" );
document.write( "the rest of the information was superfluous, since it wasn't necessary to answer the problem.\r<BR>\n" );
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document.write( "to answer the problem, all you had to do was find the area under the normal distribution curve to the left of a score of 83.<BR>\n" );
document.write( "the z-score was (83 - 80) / 3 = 1<BR>\n" );
document.write( "the area to the left of a z-score of 1 was .841345.<BR>\n" );
document.write( "that's 84.1345%.<BR>\n" );
document.write( "that would be your answer, without any further analysis.<BR>\n" );
document.write( "it was not necessary to determine the number of students, like i attempted to do.<BR>\n" );
document.write( "in fact, i'm kind of sorry i did go the extra mile.\r<BR>\n" );
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document.write( "i would recommend going with 84.1345% rounded to whatever number of decimal points required.\r<BR>\n" );
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document.write( "let me know how you did with that.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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