document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203897>Question 1203897</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 7.8 inches and standard deviation of 2.6 inches. If a sample of 49 items are chosen at random, what is the probability the sample's mean length is greater than 8.8 inches? Round answer to four 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 #839826 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=839826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population mean = 7.8<BR>\n" );
document.write( "population standard deviation = 2.6<BR>\n" );
document.write( "sample size = 49<BR>\n" );
document.write( "sample mean = 8.8\r<BR>\n" );
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document.write( "standard error = population standard deviation / sqrt(sample size) = 2.6 / sqrt(49) = .37143.\r<BR>\n" );
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document.write( "use z = (x-m)/s formula.<BR>\n" );
document.write( "z = z-score<BR>\n" );
document.write( "x is sample mean<BR>\n" );
document.write( "m = population mean<BR>\n" );
document.write( "s = standard error\r<BR>\n" );
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document.write( "formula becomes z = (8.8-7.8)/.37143 = 2.692297.\r<BR>\n" );
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document.write( "area to the right of that z-score = .003548.<BR>\n" );
document.write( "round to .0035.<BR>\n" );
document.write( "there is a 3.5% probability that the z-score wil be more than 8.8.\r<BR>\n" );
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document.write( "here's what the results look like using the calculator 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( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092621.jpg\">\r<BR>\n" );
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document.write( "the calculator can do it from the z-score or the raw score.<BR>\n" );
document.write( "if z-score, mean = 0 and standard deviation = 1.<BR>\n" );
document.write( "if raw score, mean = 7.8 and standard deviation = standard error of .37143.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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