document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=754102>Question 754102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Grade point averages of math majors at a large distance education university are normally distributed with a mean of u= 2.85 and a standard deviation of &#963;=0.30. <BR>\n" );
document.write( "If a random sample of 25 math majors is selected from that university, what is the probability that the sample mean grade point averages will be<BR>\n" );
document.write( "a) either less than 2.709 \r<BR>\n" );
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document.write( "Stanbon answered:<BR>\n" );
document.write( "t(2.709) = (2.709-2.85)/[0.3/sqrt(25)] = -2.35<BR>\n" );
document.write( "P(x < 2.709) = P(t < -2.35) = tcdf(-100,-2.35,24) = 0.0137<BR>\n" );
document.write( " <BR>\n" );
document.write( "I don't under how 0.0137 was calculated. Why isn't the solution this:<BR>\n" );
document.write( "z=-2.35 (calculated above)  so P (z<-2.35)=0.0094 <<found from normal table </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458776 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=458776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Grade point averages of math majors at a large distance education university are normally distributed with a mean of u= 2.85 and a standard deviation of &#963;=0.30. <BR>\n" );
document.write( "If a random sample of 25 math majors is selected from that university, what is the probability that the sample mean grade point averages will be<BR>\n" );
document.write( "a) either less than 2.709 \r<BR>\n" );
document.write( "\n" );
document.write( "Stanbon answered:<BR>\n" );
document.write( "t(2.709) = (2.709-2.85)/[0.3/sqrt(25)] = -2.35<BR>\n" );
document.write( "P(x < 2.709) = P(t < -2.35) = tcdf(-100,-2.35,24) = 0.0137<BR>\n" );
document.write( " <BR>\n" );
document.write( "I don't under how 0.0137 was calculated. Why isn't the solution this:<BR>\n" );
document.write( "z=-2.35 (calculated above)  so P (z<-2.35)=0.0094 <<found from normal table<BR>\n" );
document.write( "----<BR>\n" );
document.write( "You are correct if you use a z-distribution.  If that is what<BR>\n" );
document.write( "your text calls for, use it.  <BR>\n" );
document.write( "Many texts call for use of the t-distribution when dealing<BR>\n" );
document.write( "with sample means.<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============================ </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );