document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135014>Question 1135014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A worldwide organization of academics claims that the mean IQ score of its members is 115<BR>\n" );
document.write( ", with a standard deviation of 16<BR>\n" );
document.write( ". A randomly selected group of 40<BR>\n" );
document.write( " members of this organization is tested, and the results reveal that the mean IQ score in this sample is 115.8<BR>\n" );
document.write( ". If the organization's claim is correct, what is the probability of having a sample mean of 115.8<BR>\n" );
document.write( " or less for a random sample of this size? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752546 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=752546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z-score formula is 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 raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "the formula for standard error is s = sd / sqrt(n)\r<BR>\n" );
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document.write( "sd is the standard deviation of the population.<BR>\n" );
document.write( "sqrt(n) is the square root of the sample size.\r<BR>\n" );
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document.write( "the claim is that the population has a mean of 115 with a standard deviation of 16.\r<BR>\n" );
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document.write( "the sample of 40 members has a mean of 115.8.\r<BR>\n" );
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document.write( "the standard error for the distribuion of sample means is equal to 16 / sqrt(40) which is equal to 2.529822128.\r<BR>\n" );
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document.write( "the z-score for the sample mean compared to the population mean would be equal to (115.8 - 115) / 2.529822128 which is equal to .316227766.\r<BR>\n" );
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document.write( "the probability of having a sample mean of 15.8 or lessfor a random sample of this size would be the area under the normal distribution curve to the left of a z-score of .316227766.\r<BR>\n" );
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document.write( "using the z-score calculator on the TI-84 Plus, i get this area to be equal to .6240851183.\r<BR>\n" );
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document.write( "the probability of getting a sample of size 40 with a mean less than 115.8 is approximately 62.41%.\r<BR>\n" );
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document.write( "this can be seen visually through the use of the following online normal distribution calculator.\r<BR>\n" );
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document.write( "<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( "here's a picture of the results.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/021821.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "calculation of the standard error correctly is critical to getting the right probability.\r<BR>\n" );
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document.write( "standard error = standard deviation of the population divided by the square root of the sample size.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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