document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165213>Question 1165213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $136,000. This distribution follows the normal distribution with a standard deviation of $36,000.\r<BR>\n" );
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document.write( "If we select a random sample of 78 households, what is the standard error of the mean? (Round your answer to the nearest whole number.)\r<BR>\n" );
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document.write( "What is the expected shape of the distribution of the sample mean?\r<BR>\n" );
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document.write( "What is the likelihood of selecting a sample with a mean of at least $141,000? (Round your z value to 2 decimal places and final answer to 4 decimal places.)\r<BR>\n" );
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document.write( "What is the likelihood of selecting a sample with a mean of more than $131,000? (Round your z value to 2 decimal places and final answer to 4 decimal places.)\r<BR>\n" );
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document.write( "Find the likelihood of selecting a sample with a mean of more than $131,000 but less than $141,000. (Round your 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 #789774 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=789774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. SEM is 36000/sqrt(78)=$4076.20<BR>\n" );
document.write( "b. A sample from a normal distribution may be considered normal as well. The curve is narrower and steeper, as the variance is much less than for an individual.<BR>\n" );
document.write( "c.the z would be 5000/4076.20 or 1.23.  That would be 0.1093<BR>\n" );
document.write( "d. c would also be the answer for < 131000, so the answer to d is 0.8997, the complement<BR>\n" );
document.write( "e. Here, the z value is between -1.23 and +1.23, and that probability is 0.7813 </SPAN>\n" );
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