document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468888>Question 468888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i really need some help with this problem, I am really struggling with it.\r<BR>\n" );
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document.write( "Information from the American Institute of Insurance indicates the mean amount of life<BR>\n" );
document.write( "insurance per household in the United States is $110,000. This distribution follows the<BR>\n" );
document.write( "normal distribution with a standard deviation of $40,000.<BR>\n" );
document.write( "a. If we select a random sample of 50 households, what is the standard error of the mean?<BR>\n" );
document.write( "b. What is the expected shape of the distribution of the sample mean?<BR>\n" );
document.write( "c. What is the likelihood of selecting a sample with a mean of at least $112,000?<BR>\n" );
document.write( "d. What is the likelihood of selecting a sample with a mean of more than $100,000?<BR>\n" );
document.write( "e. Find the likelihood of selecting a sample with a mean of more than $100,000 but less<BR>\n" );
document.write( "than $112,000. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321698 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=321698\">put this solution on YOUR website!</A><BR><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 $110,000. <BR>\n" );
document.write( "This distribution follows the normal distribution with a standard deviation of $40,000.<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "a. If we select a random sample of 50 households, what is the standard error of the mean?<BR>\n" );
document.write( "Ans: s = 40,000/sqrt(50) = 5656.85<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( "Ans: normal<BR>\n" );
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document.write( "c. What is the likelihood of selecting a sample with a mean of at least $112,000?<BR>\n" );
document.write( "t(112,000) = (112,000-110,000)/[5656.85 = 0.3536<BR>\n" );
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document.write( "P(x-bar >= 112,000) = P(t >= 0.3536 when df = 49) = 0.3626<BR>\n" );
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document.write( "d. What is the likelihood of selecting a sample with a mean of more than $100,000?<BR>\n" );
document.write( "t(100,000) = (100,000-112,000)/5656.85 = -2.1213<BR>\n" );
document.write( "P(x-bar > 100,000) = P(t > -2.1213 when df = 49) = 0.9805<BR>\n" );
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document.write( "e. Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000.<BR>\n" );
document.write( "P(100,000 < x-bar < 112,000) = P(-2.1213 < t < 0.3626 when df=49) = 0.6213<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=============<BR>\n" );
document.write( " </SPAN>\n" );
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