document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=926144>Question 926144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a certain university the cumulative grade point average (CGPA) of first year students usually averages 2.48 with a standard deviation 0.42 . It has been found that the marks are usually approximately normally distributed. <BR>\n" );
document.write( "a) What is the probability that a student will have a CGPA that is between 1 and 3 ?   \r<BR>\n" );
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document.write( "b) What percent of students will be on probation, i.e. their CGPA is less than 2 ? \r<BR>\n" );
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document.write( "c) Academic scholarships are awarded to the top 5% of first year students. What minimum CGPA is needed to receive a scholarship?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562055 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=562055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At a certain university the cumulative grade point average (CGPA) of first year students usually averages 2.48 with a standard deviation 0.42 . It has been found that the marks are usually approximately normally distributed. <BR>\n" );
document.write( "a) What is the probability that a student will have a CGPA that is between 1 and 3 ?<BR>\n" );
document.write( "z(1) = (1-2.48)/0.42 =  -3.5238<BR>\n" );
document.write( "z(3) = (3-2.48)/0.42 =  1.2381<BR>\n" );
document.write( "----<BR>\n" );
document.write( "P(1< x < 3) = P(-3.5238 < z < 1.2381) = normalcdf(-3.5338,1.2381) = 0.8920<BR>\n" );
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document.write( " b) What percent of students will be on probation, i.e. their CGPA is less than 2 ?<BR>\n" );
document.write( "z(2) = (2-2.48)/0.42 = -1.1429<BR>\n" );
document.write( "P(x < 2) = P(z < -1.1429) = normalcdf(-100,-1.1429) = 0.1265<BR>\n" );
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document.write( " c) Academic scholarships are awarded to the top 5% of first year students. What minimum CGPA is needed to receive a scholarship?<BR>\n" );
document.write( "Find the z-value with a right-tail of 0.05<BR>\n" );
document.write( "invnorm(0.95) = 1.645<BR>\n" );
document.write( "Find the corresponding score::<BR>\n" );
document.write( "x = 1.645*0.42 + 2.48 = 3.1708<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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