document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172801>Question 1172801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Grade point averages of students on a large campus<BR>\n" );
document.write( "follow a normal distribution with a mean of 2.6 and a<BR>\n" );
document.write( "standard deviation of 0. 5.<BR>\n" );
document.write( "a. One student is chosen at random from this cam-<BR>\n" );
document.write( "pus. What is the probability that this student has a<BR>\n" );
document.write( "grade point average higher than 3.0?<BR>\n" );
document.write( "b. One student is chosen at random from this cam-<BR>\n" );
document.write( "pus. What is the probability that this student has a<BR>\n" );
document.write( "grade point average between 2.25 and 2.75?<BR>\n" );
document.write( "c. What is the minimum grade point average needed<BR>\n" );
document.write( "for a student's grade point average to be among<BR>\n" );
document.write( "the highest 10% on this campus?<BR>\n" );
document.write( "d. A random sample of 400 students is chosen from<BR>\n" );
document.write( "this campus. What is the probability that at least 80<BR>\n" );
document.write( "of these students have grade point averages higher<BR>\n" );
document.write( "than 3.0?<BR>\n" );
document.write( "e. Two students are chosen at random from this<BR>\n" );
document.write( "campus. What is the probability that at least one of<BR>\n" );
document.write( "them has a grade point average higher than 3.0? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798024 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=798024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( ">(3.0-2.6)/0.5 or >0.8. Note; > or >= are the same since this is area from a given dimensionless point on the curve.<BR>\n" );
document.write( "probability is 0.2119<BR>\n" );
document.write( "-<BR>\n" );
document.write( "this is z between -0.7 and +0.3 is 0.3759. Also 2nd VARS2Normalcdf(2.25,2.75,2.6,0.5)ENTER<BR>\n" );
document.write( "-<BR>\n" );
document.write( "the highest 10% is where z=1.282<BR>\n" );
document.write( "1.282=(x-2.6)/0.5<BR>\n" );
document.write( "0.641=x-2.6<BR>\n" );
document.write( "x=3.241<BR>\n" );
document.write( "-<BR>\n" );
document.write( "The probability of 1 being > 3.0 is 0.21185<BR>\n" );
document.write( "for 80/400 or 0.2, do a 1 proportion z test<BR>\n" );
document.write( "z>(0.2-0.21185)/sqrt(0.21185*0.78815/400)<BR>\n" );
document.write( "z>-0.01185/0.0204=-0.5801<BR>\n" );
document.write( "that probability is 0.7191 (calculator gives 0.7190)<BR>\n" );
document.write( "-<BR>\n" );
document.write( "What is the probability that neither has that value?  That is 0.7881^2 or 0.6211. So the answer is the complement of that value or 0.3789<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );