document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1024705>Question 1024705</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A researcher reports survey results by stating that the standard error of the mean is 20. The population standard deviation is 500.\r<BR>\n" );
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document.write( "a) How large was the sample used in this survey?<BR>\n" );
document.write( "b) What is the probability that the point estimate was within ±25 of the population mean? \r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "a) 625<BR>\n" );
document.write( "b) 0.7888 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640125 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=640125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sd = 500<BR>\n" );
document.write( "se = 20<BR>\n" );
document.write( "n = sample size\r<BR>\n" );
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document.write( "the formula for standard error of the mean is:\r<BR>\n" );
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document.write( "se = sd / sqrt(n)\r<BR>\n" );
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document.write( "se = 20<BR>\n" );
document.write( "sd = 500\r<BR>\n" );
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document.write( "formula becomes 20 = 500 / sqrt(n).\r<BR>\n" );
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document.write( "solve for sqrt(n) to get sqrt(n) = 500 / 20 = 25.\r<BR>\n" );
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document.write( "solve for n to get n = 25^2 = 625.\r<BR>\n" );
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document.write( "the formula for z-score is z = (x-m) / se.\r<BR>\n" );
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document.write( "(x-m) is equal to plus or minus 25.<BR>\n" );
document.write( "se is equal to 20.\r<BR>\n" );
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document.write( "the formula for z-score becomes z = plus or minus 25/20.\r<BR>\n" );
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document.write( "this results in z-score = plus or minus 1.25.\r<BR>\n" );
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document.write( "use a z-score calculator to find that the z-score between -1.25 and 1.25 has a probability of occurrence of .788...\r<BR>\n" );
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document.write( "these solutions agree with the answers provided to you.\r<BR>\n" );
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document.write( "you could assume the mean is any number.<BR>\n" );
document.write( "if the actual score is plus or minus 25 from that, you will get the same result.<BR>\n" );
document.write( "this assumes the standard error is 20.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume the mean is 5000.<BR>\n" );
document.write( "assume the actual score is 4975 or 5025.\r<BR>\n" );
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document.write( "the z-score formula becomes z = (5025 - 5000) / 20 = 25/20 = 1.25.\r<BR>\n" );
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document.write( "the z-score formula also becomes z = (4975 - 5000) / 20 = -25/20 = -1.25.\r<BR>\n" );
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document.write( "the z-wscore table between a z-score of -1.25 and 1.25 will tell you that the probbility of this occuring is .788....\r<BR>\n" );
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document.write( "here's a picture of just what i told you.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/031303.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "this solution depends on the standard error of the mean being 20.\r<BR>\n" );
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document.write( "as an additional note, the standard error of the mean is equal to the standard deviation of the distribution of sample means from multiple samples of the same sample size.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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