document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091883>Question 1091883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CRA CDs Inc. wants the mean lengths of the \"cuts\" on a CD to be 145 seconds (2 minutes and 25 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with a population standard deviation of 10 seconds. Suppose we select a sample of 24 cuts from various CDs sold by CRA CDs Inc.<BR>\n" );
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document.write( "a.	What can we say about the shape of the distribution of the sample mean?<BR>\n" );
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document.write( "  Sample mean	<BR>\n" );
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document.write( "b.	What is the standard error of the mean? (Round your z-value to 2 decimal places and final answer to 2 decimal places.)<BR>\n" );
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document.write( "  Standard error of the mean	<BR>\n" );
document.write( " seconds.  <BR>\n" );
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document.write( "c.	<BR>\n" );
document.write( "What percent of the sample means will be greater than 150 seconds? (Round your z-value to 2 decimal places and final answer to 2 decimal places.)<BR>\n" );
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document.write( "  Percent	<BR>\n" );
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document.write( "d.	<BR>\n" );
document.write( "What percent of the sample means will be greater than 138 seconds? (Round your answer to 2 decimal places.)<BR>\n" );
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document.write( "e.	<BR>\n" );
document.write( "What percent of the sample means will be greater than 138 but less than 150 seconds? (Round your z-value to 2 decimal places and final answer to 2 decimal places.)<BR>\n" );
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document.write( "  Percent	<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 #707116 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. The sample mean is normally distributed with a smaller standard deviation and the same mean as the population, 2m25s<BR>\n" );
document.write( "b. The standard error of the mean is sigma/sqrt (n)=10 sec/sqrt(24)=2.04 sec. The std error is the std deviation of the sample. There is no z-value involved here.<BR>\n" );
document.write( "c. z > 2.45(xbar-mean)/SE=(150-145)/2.04. This would be 0.71% or 0.0071<BR>\n" );
document.write( "d. z > (138-145)/2.04=-7/2.04 or z > -3.43 or 99.97% or 0.9997<BR>\n" );
document.write( "d. z>150 sec is 0.0071 from above, so we would subtract that from d to get 0.9926 or 99.26%.<BR>\n" );
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