document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=664958>Question 664958</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CRA CDs Inc. wants the mean lengths of the \"cuts\" on a CD to be 135seconds (2 min 15 sec). 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 8 seconds. Suppose we select a sample of 16 cuts from various CDs sold by CRA CDs Inc.\r<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" );
document.write( "b) What is the standard error of the mean?<BR>\n" );
document.write( "c) What percent of the sample means will be greater than 140 seconds?<BR>\n" );
document.write( "d) What percent of the sample means will be greater than 128 seconds?<BR>\n" );
document.write( "e) What percent of the sample means will be greater than 128 but less than 140 seconds?\r<BR>\n" );
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document.write( "This is just one sample problem for my homework. I cannot seem to understand the process to answering these questions. Please show all formulas and calculations so that I can learn from this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413635 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=413635\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> CRA CDs Inc. wants the mean lengths of the \"cuts\" on a CD to be 135seconds (2 min 15 sec). 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 8 seconds. Suppose we select a sample of 16 cuts from various CDs sold by CRA CDs Inc. <BR>\n" );
document.write( "a) What can we say about the shape of the distribution of the sample mean?<BR>\n" );
document.write( "According to the Central Limit Theorem:<BR>\n" );
document.write( "The mean of the sample means = the mean of the population = 135 sec<BR>\n" );
document.write( "The std of the sample means = 8/sqrt(16) = 4<BR>\n" );
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document.write( "b) What is the standard error of the mean?<BR>\n" );
document.write( "standard error = std of the sample means = 4<BR>\n" );
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document.write( "c) What percent of the sample means will be greater than 140 seconds?<BR>\n" );
document.write( "z(140) = (140-135)/4 = 5/4<BR>\n" );
document.write( "P(x-bar > 140) = P(z > 5/4) = normalcdf(5/4,100) = 0.1056<BR>\n" );
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document.write( "d) What percent of the sample means will be greater than 128 seconds?<BR>\n" );
document.write( "z(128) = (128-135)/4 = -7/4<BR>\n" );
document.write( "P(x-bar > 128) = P(z > -7/4) = normalcdf(-7/4,100) = 0.9599<BR>\n" );
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document.write( "e) What percent of the sample means will be greater than 128 but less than 140 seconds? <BR>\n" );
document.write( "Ans: = P(-7/4 < z < 5/4) = normalcdf(-7/4,-5/4) = 0.8543<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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