document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184574>Question 1184574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.4 years, and standard deviation of 4.7 years.\r<BR>\n" );
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document.write( "If 14 items are picked at random, 2% of the time their mean life will be less than how many years?\r<BR>\n" );
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document.write( "Give your answer to one decimal place.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816100 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=816100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population mean is 14.4 years.<BR>\n" );
document.write( "population standard deviation is 4.7 years.<BR>\n" );
document.write( "sample size is 14.<BR>\n" );
document.write( "degrees of freedom = 13\r<BR>\n" );
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document.write( "based on the guideline at <a  rel=nofollow HREF= \"https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value\" target = \"_blank\">https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value</a>, you would use the t-score for this problem.\r<BR>\n" );
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document.write( "standard error = standard deviation / square root of sample size = 4.7 / sqrt(14) =  1.25613.\r<BR>\n" );
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document.write( "t-score with 2% of the area under the normal distribution curve to the left of it with 13 degrees of freedom is -2.2816.\r<BR>\n" );
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document.write( "use the t-score formula to find the raw score.\r<BR>\n" );
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document.write( "t-score formula is t = (x - m) / s\r<BR>\n" );
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document.write( "that becomes:\r<BR>\n" );
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document.write( "-2.2816 = (x - 14.4) / 1.25613.\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 1.25613 * -2.2816 + 14.4 = 11.534.\r<BR>\n" );
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document.write( "round to 1 decimal place to get 11.5.\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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