document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135362>Question 1135362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A particular fruit's weights are normally distributed, with a mean of 481 grams and a standard deviation of 9 grams.\r<BR>\n" );
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document.write( "If you pick 8 fruits at random, then 15% of the time, their mean weight will be greater than how many grams?\r<BR>\n" );
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document.write( "Give your answer to the nearest gram. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752985 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=752985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean of the population is 481 grams and the standard deviation of the population is 9 grams.\r<BR>\n" );
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document.write( "your sample size is 8.\r<BR>\n" );
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document.write( "therefore the standard deviation of the distribution of sample means, otherwise know as the standard error, is s = sdp / sqrt(ss).\r<BR>\n" );
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document.write( "s is the standard error<BR>\n" );
document.write( "sdp is the standard deviation of the population<BR>\n" );
document.write( "ss is the sample size.\r<BR>\n" );
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document.write( "s becomes equal to 9 / sqrt(8) = 3.181980515.\r<BR>\n" );
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document.write( "you need to look up the z-score for an area to the right of it being equal to .15.\r<BR>\n" );
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document.write( "this means you need to look up the z-score for an area of 1 - .15 = .85 to the left of it.\r<BR>\n" );
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document.write( "using the ti-84 plus calculator, i get a z-score with an area of .85 to the left of it equal to 1.03643338.\r<BR>\n" );
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document.write( "to find the raw score associated with this, use the z-score formula of 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( "with a mean of 481 and a standard error of 3.181980515 and a z-score of 1.03643338, this formula becomes:\r<BR>\n" );
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document.write( "1.03643338 = (x - 481) / 3.181980515.\r<BR>\n" );
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document.write( "solve for x to get x = 1.03643338 * 3.181980515 + 481 = 484.2979108.\r<BR>\n" );
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document.write( "visually, this looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/022307.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( ".85 area to the left of the value is equal to .15 area to the right of the value.\r<BR>\n" );
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document.write( "that looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/022308.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "your solution is that, if you pick a sample of 8 fruits at random, then 15% of the time their mean weight will be greater than 484.2979108 grams.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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