document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192345>Question 1192345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is σ= 9 milligrams. Juan repeats the measurement 3 times and records the mean x of his 3 measurements.\r<BR>\n" );
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document.write( "A) What is the standard deviation (±0.01) of Juan's mean result? (That is, if Juan kept on making 3 measurements and averaging them, what would be the standard deviation of all his x's?) \r<BR>\n" );
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document.write( "B) How many times must Juan repeat the measurement so that the standard deviation of x is 2?  (Round your answer to the nearest whole number.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849036 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **A) Standard Deviation of Juan's Mean Result**\r<BR>\n" );
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document.write( "* **Concept:** The standard deviation of the sample mean (x̄) is also known as the **standard error of the mean**. <BR>\n" );
document.write( "* **Formula:** Standard Error (SE) = σ / √n <BR>\n" );
document.write( "    * where σ is the population standard deviation and n is the sample size.\r<BR>\n" );
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document.write( "* **Given:** σ = 9 milligrams, n = 3 measurements\r<BR>\n" );
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document.write( "* **Calculation:** SE = 9 / √3 ≈ 5.196 milligrams\r<BR>\n" );
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document.write( "* **Standard Deviation of Juan's Mean Result:** 5.20 milligrams (rounded to 2 decimal places)\r<BR>\n" );
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document.write( "**B) Number of Measurements for Standard Deviation of x = 2**\r<BR>\n" );
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document.write( "* **Rearrange the Standard Error formula:** <BR>\n" );
document.write( "    * SE = σ / √n <BR>\n" );
document.write( "    * √n = σ / SE<BR>\n" );
document.write( "    * n = (σ / SE)²\r<BR>\n" );
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document.write( "* **Given:** σ = 9 milligrams, SE = 2 milligrams\r<BR>\n" );
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document.write( "* **Calculation:** n = (9 / 2)² = 20.25 \r<BR>\n" );
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document.write( "* **Number of Measurements:** 21 (rounded to the nearest whole number)\r<BR>\n" );
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document.write( "**In summary:**\r<BR>\n" );
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document.write( "* A) The standard deviation of Juan's mean result is 5.20 milligrams.<BR>\n" );
document.write( "* B) Juan must repeat the measurement 21 times to achieve a standard deviation of his mean result of 2 milligrams.<BR>\n" );
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