document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185730>Question 1185730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average household income in a large town is $44,500, with a standard deviation of $17,200. If a SRS of 100 households is taken, find the following.\r<BR>\n" );
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document.write( "The probability that the sample mean is between $42,000 and $48,000. Round your answer to three decimal places.\r<BR>\n" );
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document.write( "he probability that the sample mean is below $43,000. Round your answer to three decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816677 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=816677\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the key thing you have to do is get the standard error.\r<BR>\n" );
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document.write( "standard error = population standard deviation / square root of sample size.\r<BR>\n" );
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document.write( "in this problem:\r<BR>\n" );
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document.write( "standard deviation = 17,200<BR>\n" );
document.write( "sample size = 100\r<BR>\n" );
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document.write( "s = standard error = 17200 / sqrt(100) = 1720.\r<BR>\n" );
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document.write( "m = population mean = 44,500.\r<BR>\n" );
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document.write( "z = (x - m) / s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the sample mean<BR>\n" );
document.write( "m is the population mean<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "if you want to find the probability that the sample mean is between 42,000 and 48,000, then you can find the z-score for 42,000 and the z-score for 48,000, and then find the probability of getting a z-score between them.\r<BR>\n" );
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document.write( "for 42,000, z = (42000 - 44500) / 1720 = -1.4535 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "for 48,000, z = (48000 - 44500) / 1720 = 2.0349 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "the probability of getting a z-score between -1.4535 and 2.0349 is equal to .906027 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "you could also have done this directly, and gotten the same result.\r<BR>\n" );
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document.write( "the following online calculator will do the same for you, only it will round the answer to 3 decimal digits.\r<BR>\n" );
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document.write( "i used the ti-84 plus calculator to get the more detailed answer.\r<BR>\n" );
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document.write( "here's the display from the calculator to find the probability between the z-scores.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/100905.jpg\" >\r<BR>\n" );
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document.write( "here's the display from the calculator to find the probability between the raw scores.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/100906.jpg\" >\r<BR>\n" );
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document.write( "if you're looking for z-scores, then set the mean = 0 and standard deviation = 1.\r<BR>\n" );
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document.write( "if you're looking for raw scores, then use the mean and the standard error in the space that is marked as standard deviation.\r<BR>\n" );
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document.write( "when you are using the mean of a sample of a certain size, you have to use the standard error and not the standrad deviation.\r<BR>\n" );
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document.write( "the standard error is also a standard deviation, but it is the standard deviation of the distribution of sample means, which is different than the standard deviation of the sample itself.\r<BR>\n" );
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document.write( "here's a reference on standard error of the mean.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://statisticsbyjim.com/hypothesis-testing/standard-error-mean/\" target = \"_blank\">https://statisticsbyjim.com/hypothesis-testing/standard-error-mean/</a>\r<BR>\n" );
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document.write( "the online statistical calculator i used can be found at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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