document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162677>Question 1162677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random sample of size n = 72 is taken from a population with mean μ = −13.7 and standard deviation σ = 9. [You may find it useful to reference the z table.]\r<BR>\n" );
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document.write( "a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round \"expected value\" to 1 decimal place and \"standard error\" to 4 decimal places.)\r<BR>\n" );
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document.write( "b. What is the probability that the sample mean is less than −14? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)\r<BR>\n" );
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document.write( "c. What is the probability that the sample mean falls between −14 and −13? (Do not round intermediate calculations. Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)\r<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 #786620 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=786620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> E(X)= -13.7, the mean<BR>\n" );
document.write( "SE is sigma/sqrt(n)=9/sqrt(72)=1.0607<BR>\n" );
document.write( "z<(-14--13.7)/1.0607<BR>\n" );
document.write( "<-0.3/1.0607<BR>\n" );
document.write( "<-0.28. or -0.2828<BR>\n" );
document.write( "probability is 0.3897<BR>\n" );
document.write( "z for -13 is (0.7/1.0607)=0.6600\r<BR>\n" );
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document.write( "probability of z between -0.28 and 0.66 is 0.3567\r<BR>\n" );
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