document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202772>Question 1202772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 53.0% of American households still have landline phone service. We decide to randomly call eight households and ask if the home has a landline phone.\r<BR>\n" );
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document.write( "a. What is the probability that exactly five of the households in the sampled group have a landline phone service?\r<BR>\n" );
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document.write( "b. Given the probability distribution, what is the mean number of households with landline service?\r<BR>\n" );
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document.write( "c. What is the variance of the probability distribution of the number of households with landline service? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837864 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52813)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837864\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "American households increasingly rely on cell phones as their exclusive telephone service. <BR>\n" );
document.write( "It is reported that 53.0% of American households still have landline phone service. <BR>\n" );
document.write( "We decide to randomly call eight households and ask if the home has a landline phone.<BR>\n" );
document.write( "(a) What is the probability that exactly five of the households in the sampled group <BR>\n" );
document.write( "have a landline phone service?<BR>\n" );
document.write( "(b) Given the probability distribution, what is the mean number of households with landline service?<BR>\n" );
document.write( "(c) What is the variance of the probability distribution of the number of households with landline service?<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is a standard binomial distribution probability problem.<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The number of trials &nbsp;n= 8.  &nbsp;The probability of success at each individual trial is &nbsp;p= 0.53.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B8%5D%5E5%2Ap%5E5%2A%281-p%29%5E3 ALIGN=MIDDLE  ALT=\"C%5B8%5D%5E5%2Ap%5E5%2A%281-p%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%288%2A7%2A6%29%2F%281%2A2%2A3%29%29%2A0.53%5E5%2A%281-0.53%29%5E3 ALIGN=MIDDLE  ALT=\"%28%288%2A7%2A6%29%2F%281%2A2%2A3%29%29%2A0.53%5E5%2A%281-0.53%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.2431  (rounded).   <U>ANSWER</U>\r\n" );
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document.write( "(b)  the mean number of households with landline service is \r\n" );
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document.write( "         np = in this problem = 0.53*8 = 4.24  (exact value).   <U>ANSWER</U>\r\n" );
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document.write( "(c)  the variance of the probability distribution of the number of households with landline service is \r\n" );
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document.write( "         n*p*(1-p) = in this problem = 8*0.53*(1-0.53) = 1.9928  (exact value).    <U>ANSWER</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "The relevant formulas you can find in any standard textbook on the subject.\r<BR>\n" );
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document.write( "To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Learn the entire subject from there.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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