document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185779>Question 1185779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let us assume that the grades of 500 students are normally distributed with 𝜇=45 and standard deviation 𝜎=20. If the 20% of the students get excellent, what is the grade that determines the excellent? (What is 𝛸 value?) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816619 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=816619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 45<BR>\n" );
document.write( "standard deviation = 20<BR>\n" );
document.write( "number of students = 500\r<BR>\n" );
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document.write( "z-score = (x - m) / s\r<BR>\n" );
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document.write( "in this problem:\r<BR>\n" );
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document.write( "x is the number of students who get excellent.<BR>\n" );
document.write( "m is the mean = 45<BR>\n" );
document.write( "s is the standard deviation = 20\r<BR>\n" );
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document.write( "you are looking for the z-score that has 20% of the area of the normal distribution curve to the right of it.\r<BR>\n" );
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document.write( "that z-score will be equal to .8416 when rounded to 4 decimal places.\r<BR>\n" );
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document.write( "to find the raw score, use the z-score formula of z = (x - m) / s\r<BR>\n" );
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document.write( "in this formula, z = .8416, m = 45, s = 20\r<BR>\n" );
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document.write( "the formula becomes .8416 = (x - 45) / 20\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = .8416 * 20 + 45 = 61.832.\r<BR>\n" );
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document.write( "a score above that will be excellent.<BR>\n" );
document.write( "only 20% of the students will get a score greater than that.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/100803.jpg\" > </SPAN>\n" );
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