document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194651>Question 1194651</A>: <I><SPAN STYLE=\"word-break: break-all;\"> .The U.S census Bureau (Annual social and economic supplement) collects demographics <BR>\n" );
document.write( "concerning the number of people in families per household. Assume the distribution of the <BR>\n" );
document.write( "number of people per households is shown in the following probability distribution table: <BR>\n" );
document.write( "x P(x) <BR>\n" );
document.write( "2 0.27 <BR>\n" );
document.write( "3 <BR>\n" );
document.write( "4 0.28 <BR>\n" );
document.write( "5 0.13 <BR>\n" );
document.write( "6 0.04 <BR>\n" );
document.write( "7 0.03 <BR>\n" );
document.write( "a) Show that P(x=3) = 0.25 <BR>\n" );
document.write( "b) Calculate the expected number (mean) of people in families per household in the United <BR>\n" );
document.write( "States. <BR>\n" );
document.write( "c) Compute the variance and standard deviation of the number of people in families per <BR>\n" );
document.write( "household.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827631 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=827631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .The U.S census Bureau (Annual social and economic supplement) collects demographics<BR>\n" );
document.write( "concerning the number of people in families per household. Assume the distribution of the<BR>\n" );
document.write( "number of people per households is shown in the following probability distribution table:<BR>\n" );
document.write( "x P(x)<BR>\n" );
document.write( "2 0.27<BR>\n" );
document.write( "3<BR>\n" );
document.write( "4 0.28<BR>\n" );
document.write( "5 0.13<BR>\n" );
document.write( "6 0.04<BR>\n" );
document.write( "7 0.03<BR>\n" );
document.write( "a) Show that P(x=3) = 0.25\r<BR>\n" );
document.write( "\n" );
document.write( "Solution:<BR>\n" );
document.write( "The total of the probabilities must be equal to 1.<BR>\n" );
document.write( "Therefore, P(x=3) = 1-0.27-0.28-0.13-0.04-0.03= 0.25\r<BR>\n" );
document.write( "\n" );
document.write( "b) Calculate the expected number (mean) of people in families per household in the United<BR>\n" );
document.write( "States.<BR>\n" );
document.write( "To calculate the mean, multiply each value of x by the corresponding probability and get the sum.<BR>\n" );
document.write( "E(X) = 2*0.27+3*0.25+4*0.28+5*0.13+6*0.04+7*0.03=  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283.51%29 ALIGN=MIDDLE  ALT=\"highlight%283.51%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c) Compute the variance and standard deviation of the number of people in families per<BR>\n" );
document.write( "household.\r<BR>\n" );
document.write( "\n" );
document.write( "Calculate first the mean of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2 ALIGN=MIDDLE  ALT=\"X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by multiplying the square of x by the corresponding probability, and get the sum.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E2%29+ ALIGN=MIDDLE  ALT=\"E%28X%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E2%29%2A0.27%2B%283%5E2%29%2A0.25%2B%284%5E2%29%2A0.28%2B%285%5E2%29%2A0.13%2B%286%5E2%29%2A0.04%2B%287%5E2%29%2A0.03 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = 13.97\r<BR>\n" );
document.write( "\n" );
document.write( "The variance is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28X%5E2%29+-+%28E%28X%29%29%5E2 ALIGN=MIDDLE  ALT=\"E%28X%5E2%29+-+%28E%28X%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.97-3.51%5E2 ALIGN=MIDDLE  ALT=\"13.97-3.51%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281.6499%29 ALIGN=MIDDLE  ALT=\"highlight%281.6499%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The standard deviation is equal to the square root of the variance which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281.284484%29 ALIGN=MIDDLE  ALT=\"highlight%281.284484%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "You can email me (reviewermath yahoo) if you need one-one-one tutoring in Statistics and Probability through the whiteboard.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );