document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184550>Question 1184550</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer knows that their items have a normally distributed length, with a mean of 5.5 inches, and standard deviation of 0.7 inches.\r<BR>\n" );
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document.write( "If 5 items are chosen at random, what is the probability that their mean length is less than 4.7 inches? (Give answer to 4 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 #816089 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=816089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sample size is 5.\r<BR>\n" );
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document.write( "if you follow this guide as to when to use the t-score or when to use the z-score, you will find that the use of the t-score is indicated in this problem.\r<BR>\n" );
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document.write( "<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>\r<BR>\n" );
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document.write( "i'll do both to show you the difference.\r<BR>\n" );
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document.write( "the population mean is 5.5 inches.<BR>\n" );
document.write( "the population standard deviation is .7 inches.\r<BR>\n" );
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document.write( "the standard error = population standard deviation / square root of sample size = .7 / sqrt(5) = .31305.\r<BR>\n" );
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document.write( "the t-score is equal to (x - m) / s = (4.7 - 5.5) / .31305 = -2.5555.\r<BR>\n" );
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document.write( "the test t-score with 4 degrees of freedom give you an area of .0314687 to the left of that z-score.\r<BR>\n" );
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document.write( "your probability that the mean length is less than 4.7 inches is equal to .0315 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "the z-score is also equal to -2.5555.\r<BR>\n" );
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document.write( "the probability of getting a z-score less than -2.5555 is equal to .0053.\r<BR>\n" );
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document.write( "here's a reference on the relative shape of the t-score, depending on the degrees of freedom.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.statisticshowto.com/t-statistic/\" target = \"_blank\">https://www.statisticshowto.com/t-statistic/</a>\r<BR>\n" );
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document.write( "the t-score begins to look more like the z-score as the sample size goes up.<BR>\n" );
document.write( "at the lower end of sample sizes, the difference is more pronounced.\r<BR>\n" );
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document.write( "your solution in this problem is that the probability of getting a score less than 4.7 is equal to .0315 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "this assumes use of the t-score.\r<BR>\n" );
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document.write( "if the use of the z-score is assumed, than the probability is .0053.\r<BR>\n" );
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document.write( "i would go with the assumption of t-score, unless otherwise instructed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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