document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161981>Question 1161981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average grade of a subject is 1.89 for the whole class, with a standard deviation of 0.63. If a sample is 25 students is being taken, then find the probability of getting the average of this sample to be within the range of 1.6 and 2.0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785644 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=785644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw mean<BR>\n" );
document.write( "n is the sample size<BR>\n" );
document.write( "s is the standard deviation of the distribution of sample means<BR>\n" );
document.write( "sd is the standard deviation of the population, or the sample, if the standard deviation of the population is not available.<BR>\n" );
document.write( "if the standard deviation of the population is known, use the z-score, else use the t-score.\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "m = 1.89<BR>\n" );
document.write( "sd = .63<BR>\n" );
document.write( "n = 25\r<BR>\n" );
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document.write( "s = sd / sqrt(n) = .63 / sqrt(25) = .126\r<BR>\n" );
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document.write( "use the z-score formula to find the z-scores.<BR>\n" );
document.write( "that formula is z = (x - m) / s<BR>\n" );
document.write( "for a raw score of 1.6, that formula becomes:<BR>\n" );
document.write( "z = (1.6 - 1.89) / .126 = -2.30 rounded to 2 decimal places.<BR>\n" );
document.write( "for a raw score of 2.0, tha formula becomes:<BR>\n" );
document.write( "z = (2.0 - 1.89) / .126 = .87 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "look for the area to the left of the z-score equal to -2.30 and .87 in the z-score table.\r<BR>\n" );
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document.write( "you will find that the area to the left of each z-score is as indicated below:\r<BR>\n" );
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document.write( "for -2.30 = .01072<BR>\n" );
document.write( "for .87 = .80785\r<BR>\n" );
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document.write( "subtract the smaller area from the larger area to get the areas in between is equal to .79713.\r<BR>\n" );
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document.write( "that's the probability that the scores in this sample will be between 1.6 and 2.0.\r<BR>\n" );
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document.write( "the table i used can be found at <a  rel=nofollow HREF= \"https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf\" target = \"_blank\">https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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