document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077402>Question 1077402</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A final exam in Statistics has a mean of 73 with a standard deviation of 7.73.  Assume that a random sample of 24 students is selected and the mean test score of the sample is computed.  What percentage of sample means are less than 70?\r<BR>\n" );
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document.write( "mean of sample 7.73/sq root 24  7.73/4.9 = 1.6\r<BR>\n" );
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document.write( "z(70)= (70-73)/1.6 = -3/1.6 = -1.85\r<BR>\n" );
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document.write( "P (x<70) = P(z<-1.85) = ???\r<BR>\n" );
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document.write( "Help?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691863 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=691863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Standard Error = SE<BR>\n" );
document.write( "SE = s/sqrt(n)<BR>\n" );
document.write( "SE = 7.73/sqrt(24)<BR>\n" );
document.write( "SE = 1.57787964264283\r<BR>\n" );
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document.write( "Standard Z score<BR>\n" );
document.write( "z = (x - mu)/SE<BR>\n" );
document.write( "z = (70-73)/1.57787964264283<BR>\n" );
document.write( "z = -1.9012856994436<BR>\n" );
document.write( "z = -1.90\r<BR>\n" );
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document.write( "Now use <a  rel=nofollow HREF= \"http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf\">a table</a> to find the area to the left of z = -1.90<BR>\n" );
document.write( "With that table, look at the row that has -1.9 and the column with 0.00. The intersection of this row and column combo has 0.0287 in the cell\r<BR>\n" );
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document.write( "This means that<BR>\n" );
document.write( "P(Z < -1.90) = 0.0287<BR>\n" );
document.write( "P(xbar < 70) = 0.0287<BR>\n" );
document.write( "This is approximate of course. To get better accuracy, a calculator is recommended. \r<BR>\n" );
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document.write( "Since the area is 0.0287, the percentage of sample means less than 70 is roughly <font color=red>2.87%</font> which is the final answer.<BR>\n" );
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