document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168124>Question 1168124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Scores on a standardized exam are known to follow a normal distribution with a standard deviationσ of = 8.  A researcher randomly selects 84 students and finds their mean exam score to be (X with the bar over it) = 78. How confident are you that the mean score for all students taking the exam is in the interval (76.702, 79.298)?<BR>\n" );
document.write( "confidence level= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792744 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> standard deviation of the population is 8.<BR>\n" );
document.write( "sample size is 84.<BR>\n" );
document.write( "sample mean is 78.\r<BR>\n" );
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document.write( "the standard error is equal to the population standard deviation divided by the sample size.\r<BR>\n" );
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document.write( "this is equal to 8 / sqrt(84) = .8728715609\r<BR>\n" );
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document.write( "use a normal distribution calculator to find the proportion of scores between 76.702 and 79.298 when the mean score is 78 and the standard error of a sample size of 84 is equal to .8728715609.\r<BR>\n" );
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document.write( "your result will be that the proportion is equal to .8629972264.\r<BR>\n" );
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document.write( "that's your confidence level.\r<BR>\n" );
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document.write( "you are confident that 86.3% of samples of size 84 will have a mean that falls between 76.702 and 79.298.\r<BR>\n" );
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document.write( "100 - 86.3 = 13.7% of the samples will have a mean that falls outside these limits.\r<BR>\n" );
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document.write( "half of the 13.7% will fall below 76.782 and the other half of the 13.7% will fall above 79.298.\r<BR>\n" );
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document.write( "here's a display of the calculator results, rounded to whatever rounding rules the calculator has.\r<BR>\n" );
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document.write( "the online calculator says that the probability that the scores will be within those limits is .863.\r<BR>\n" );
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document.write( "round .8629972264. to 3 decimal digits and it becomes .863.\r<BR>\n" );
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document.write( "that online calculator can be found at <a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "that calculator rounds the results to .863.\r<BR>\n" );
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document.write( "the TI-84 Plus calculator that i use (a physical calculator, not an online calculator, gave me the results rounded to a lot more decimal digits.\r<BR>\n" );
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document.write( "it does not, however, provided a nice online display such as the display from the online calculator.\r<BR>\n" );
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