document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094890>Question 1094890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1-Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that no more than 3 customers would be willing to switch their cable?<BR>\n" );
document.write( "Answer 0.85 0.15 0.20 0.411 0.589\r<BR>\n" );
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document.write( "I know the answer is .411 but have no idea how I got there. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #709510 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=709510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>This is a straightforward application of the binomial formula.  If the probability is .2 that each customer is willing to switch and .8 that they are not, then the probability that n of the 20 customers will be willing to switch is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2820%2Cn%29%2A%28.8%5En%29%2A%28.2%5E%2820-n%29%29 ALIGN=MIDDLE  ALT=\"C%2820%2Cn%29%2A%28.8%5En%29%2A%28.2%5E%2820-n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where \"C(20,n)\" is \"20 choose n\".<br><BR>\n" );
document.write( "Since you want the probability that no more than 3 of the 20 customers will be willing to change plans, the calculations you need to perform are...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2820%2C0%29%2A%28.8%5E20%29%2A%28.2%5E0%29 ALIGN=MIDDLE  ALT=\"C%2820%2C0%29%2A%28.8%5E20%29%2A%28.2%5E0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [0 willing to switch];<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2820%2C1%29%2A%28.8%5E19%29%2A%28.2%5E1%29 ALIGN=MIDDLE  ALT=\"C%2820%2C1%29%2A%28.8%5E19%29%2A%28.2%5E1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1 willing to switch];<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2820%2C2%29%2A%28.8%5E18%29%2A%28.2%5E2%29 ALIGN=MIDDLE  ALT=\"C%2820%2C2%29%2A%28.8%5E18%29%2A%28.2%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2 willing to switch]; and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2820%2C3%29%2A%28.8%5E17%29%2A%28.2%5E3%29 ALIGN=MIDDLE  ALT=\"C%2820%2C3%29%2A%28.8%5E17%29%2A%28.2%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [3 willing to switch]<br><BR>\n" );
document.write( "Then of course you need to add the probabilities for those 4 cases.<br><BR>\n" );
document.write( "The calculations are tedious with pencil and paper, and even with a scientific calculator; a spread sheet works nicely.<br><BR>\n" );
document.write( "And .411 is the right answer....<BR>\n" );
document.write( " </SPAN>\n" );
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