document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171891>Question 1171891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Many U.S. households still do not have Internet access. Suppose 25 out of 80 households in a small southern town do not have Internet access. A company that provides high-speed Internet has recently entered the market. As part of the marketing campaign, the company decides to randomly select ten households and offer them red laptops along with a brochure that describes their services.  The aim is to build goodwill and, with a free laptop, tempt nonusers into getting Internet access.<BR>\n" );
document.write( "a.	What is the probability that six laptop recipients do not have Internet access? <BR>\n" );
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document.write( "b.	What is the probability that at least five recipients do not have Internet access? <BR>\n" );
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document.write( "c.	What is the probability that two or fewer laptop recipients do not have Internet access?<BR>\n" );
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document.write( "d.	What is the expected number of laptop recipients who do not have Internet access?<BR>\n" );
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document.write( "e.	Calculate the expected value, the variance, and the standard deviation for the recipients who do not have Internet access.<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 #797203 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=797203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: I am assuming the 80 households is the entire population and the sampling of one item changes the distribution significantly for the next item.  We have a fixed number of houses sampled (10), but not a constant probability for each one, with the way the problem is worded. This is different from saying 25 of every 80 households. This is a hypergeometric distribution in other words.\r<BR>\n" );
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document.write( "80C10 are the number of ways to choose 10 from 80. That is the denominator <BR>\n" );
document.write( "The numerator for a is 25C6*55C4<BR>\n" );
document.write( "The probability is 0.0367<BR>\n" );
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document.write( "at least 5 do not have access. Look at 7 do not have:0.0077 using the same approach. And for 8 0.0001<BR>\n" );
document.write( "9 and 10 are <0.0001, 5 do not have access is 0.1123. The sum (using 6 above as well) is 0.1568, the answer.<BR>\n" );
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document.write( "probability of 2 not having is 25C2*55C8/80C10 or 0.2218<BR>\n" );
document.write( "of 1 it is 25C1*55C9/80C10=0.0965<BR>\n" );
document.write( "of 0 it is 55C10/80C10=0.0178<BR>\n" );
document.write( "That sum is 0.3361<BR>\n" );
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document.write( "To do the expected value, one needs the probability * the random variable.<BR>\n" );
document.write( "9 and 10 are both 0<BR>\n" );
document.write( "3 and 4 are 25C3*55C7/80C10=0.2835<BR>\n" );
document.write( "and p(4)=0.2228<BR>\n" );
document.write( "so<BR>\n" );
document.write( "0*p(0)=0 as well as 9*p(9) and 10 p(10)<BR>\n" );
document.write( "p(1)=0.0965 and *1=0.0965<BR>\n" );
document.write( "p(2)=0.2218 and *2=0.4436<BR>\n" );
document.write( "p(3)=0.2835 and *3=0.8505<BR>\n" );
document.write( "p(4)=0.2228 and *4=0.8912<BR>\n" );
document.write( "p(5)=0.1123 and *5=0.5615<BR>\n" );
document.write( "p(6)=0.0367 and *6=0.0220<BR>\n" );
document.write( "p(7)=0.0077 and *7=0.0539<BR>\n" );
document.write( "p(8)=0.0001 and *8=0.0008<BR>\n" );
document.write( "That sum is 2.92 and that is the expected value.<BR>\n" );
document.write( "The variance and the sd (sqrt (V) ) can be done from that.<BR>\n" );
document.write( "Note: by using a binomial with a larger pool, the expected value is 3.125, but that doesn't apply given the above assumptions. </SPAN>\n" );
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