document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927344>Question 927344</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The midterm exam scores in a large stat class in a certain university is normally distributed with a mean score of 60 and a standard deviation of 12.\r<BR>\n" );
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document.write( "a. Find the probability that the student will get a score greater than 65?<BR>\n" );
document.write( "b. Find the probability that the student will get a score less than 57?<BR>\n" );
document.write( "c. If there are 200 students. How many of them got a grade of less than 55?<BR>\n" );
document.write( "d. If the highest 70% of the class passed, what is the lowest passing score? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562927 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=562927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean score of 60 and a standard deviation of 12.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+blue%28x+-+60%29%2Fblue%2812%29 ALIGN=MIDDLE  ALT=\"z+=+blue%28x+-+60%29%2Fblue%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( ".........<BR>\n" );
document.write( "P(x > 65) = P(z > 5/12) = normalcdf(.4167,100) = .3384  0r 33.84%<BR>\n" );
document.write( "......<BR>\n" );
document.write( "P(x < 57) = P(z < -3/12)= normalcdf(-100, -.25) = .4013  0r 40.13%\r<BR>\n" );
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document.write( ".........<BR>\n" );
document.write( "P(x < 55) = P(z < -5/12) = normalcdf(-100, -.4167)= .3384  <BR>\n" );
document.write( "200(.384)= 67.68,  68 got a grade of less than 55<BR>\n" );
document.write( "............<BR>\n" );
document.write( "12invNorm(.30) + 60 = X<BR>\n" );
document.write( "X = 12(-.5244) + 60 = 53.7.  54 is the lowest passing score<BR>\n" );
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