document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=862717>Question 862717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (Please help me with this question?)\r<BR>\n" );
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document.write( "Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $120,000. This distribution follows the normal distribution with a standard deviation of $38,000.\r<BR>\n" );
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document.write( "(a)	<BR>\n" );
document.write( "If we select a random sample of 58 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( "  Standard error of the mean=?\r<BR>\n" );
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document.write( "(b)	What is the expected shape of the distribution of the sample mean?<BR>\n" );
document.write( " 	 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "	Not normal, the standard deviation is unknown.<BR>\n" );
document.write( "	Unknown.<BR>\n" );
document.write( "	Uniform<BR>\n" );
document.write( "	Normal.<BR>\n" );
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document.write( "(c)	<BR>\n" );
document.write( "What is the likelihood of selecting a sample with a mean of at least $124,000? (Round z value to 2 decimal places and final answer to 4 decimal places.)\r<BR>\n" );
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document.write( "  Probability=?  \r<BR>\n" );
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document.write( "(d)	<BR>\n" );
document.write( "What is the likelihood of selecting a sample with a mean of more than $112,000? (Round z value to 2 decimal places and final answer to 4 decimal places.)\r<BR>\n" );
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document.write( "  Probability=? \r<BR>\n" );
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document.write( "(e)	<BR>\n" );
document.write( "Find the likelihood of selecting a sample with a mean of more than $112,000 but less than $124,000. (Round z value to 2 decimal places and final answer to 4 decimal places.)\r<BR>\n" );
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document.write( "  Probability=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #519978 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=519978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) standard error of the mean = 38000 / square root(56) = 5078<BR>\n" );
document.write( "b) normal<BR>\n" );
document.write( "c) P(x > or = 124000) = 1 - P(x<124000)<BR>\n" );
document.write( "we calculate the z score for P(x<124000)<BR>\n" );
document.write( "124000 - 120000 / 5078 = 0.78771169751870815282 = 0.79<BR>\n" );
document.write( "consult z table for probability assocated with z score = .79<BR>\n" );
document.write( "P(x > or = 124000) = 1 - .79 = 0.21<BR>\n" );
document.write( "d) P(x > or = 112000) = 1 - P(x<112000)<BR>\n" );
document.write( "we calculate the z score for P(x<112000)<BR>\n" );
document.write( "112000 - 120000 / 5078 = -1.58<BR>\n" );
document.write( "consult -z table for probability assocated with z score = -1.58<BR>\n" );
document.write( "P(x > 112000) = 1 - P(x<112000) = 1 - 0.06 = 0.94<BR>\n" );
document.write( "e) P(x > 112000 and x < 124000) = P(x<124000) - P(x<112000) = 0.79 - 0.06 = 0.73\r<BR>\n" );
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document.write( " </SPAN>\n" );
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