document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288143>Question 288143</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to the US Census Bureau, roughly 14.5% of individuals are living below the poverty level. Suppose a random sample of 500 individuals was taken. <BR>\n" );
document.write( "a.  Describe the sampling distribution of p-hat, the sample proportion of individuals living below the poverty level.\r<BR>\n" );
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document.write( "        1.  The mean of p-hat is:_________\r<BR>\n" );
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document.write( "        2.  The standard error of p-hat is:_________\r<BR>\n" );
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document.write( "3.  In a random sample of 500 individuals, find the probability that no more than 10% are living below the poverty level.<BR>\n" );
document.write( "What is the probability that a random sample of 500 individuals results in 80 or more having an advanced degree? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208847 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=208847\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  According to the US Census Bureau, roughly 14.5% of individuals are living below the poverty level.<BR>\n" );
document.write( "Suppose a random sample of 500 individuals was taken. <BR>\n" );
document.write( "a. Describe the sampling distribution of p-hat, the sample proportion of individuals living below the poverty level. <BR>\n" );
document.write( "1. The mean of p-hat is: 14.5% according to the Central Limit Theorem<BR>\n" );
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document.write( "2. The standard error of p-hat is: sqrt(0.145*0.855/500) = 0.0157 according to CLT<BR>\n" );
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document.write( "3. In a random sample of 500 individuals, find the probability that no more than 10% are living below the poverty level.<BR>\n" );
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document.write( "Find the z-value that has a left tail of 10%: z = -1.2816..<BR>\n" );
document.write( "Find the x-value associated with z = -1.2816<BR>\n" );
document.write( "x = -1.2816*0.0157+ 0.145 <BR>\n" );
document.write( "x = 0.1249 <BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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