document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202771>Question 1202771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Statistics from the Port Authority of New York and New Jersey show that 70% of the vehicles using the Lincoln Tunnel that connects New York City and New Jersey use E-ZPass to pay the toll rather than stopping at a toll booth. Twelve cars are randomly selected.\r<BR>\n" );
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document.write( "a. How many of the 12 vehicles would you expect to use E-ZPass?  <BR>\n" );
document.write( "b. What is the mode of the distribution? What is the probability associated with the mode? (Hint: Mode is the value of X with the highest probability)<BR>\n" );
document.write( "c. What is the probability three or more of the sampled vehicles use E-ZPass? \r<BR>\n" );
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document.write( "Transponder<BR>\n" );
document.write( "0<BR>\n" );
document.write( "1<BR>\n" );
document.write( "2<BR>\n" );
document.write( "3<BR>\n" );
document.write( "4<BR>\n" );
document.write( "5<BR>\n" );
document.write( "6<BR>\n" );
document.write( "7<BR>\n" );
document.write( "8<BR>\n" );
document.write( "9<BR>\n" );
document.write( "10<BR>\n" );
document.write( "11<BR>\n" );
document.write( "12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840415 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=840415\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It's a binomial with n=12 and p=0.7<BR>\n" );
document.write( "the expected value is 8.4 That answers the first part.<BR>\n" );
document.write( "For probability of 3 or more, do 1-prob (0,1,2)<BR>\n" );
document.write( "prob of 0=0.3^12=0 essentially <BR>\n" );
document.write( "prob of 1 is 12*0.7*0.3^11=0.00001<BR>\n" );
document.write( "prob of 2 is 12C2*0.7^2*0.3^10=0.0002<BR>\n" );
document.write( "answer is the 1-sum which is 1-0.0002=0.9998<BR>\n" );
document.write( "-<BR>\n" );
document.write( "can check the mode 12C8*0.7^8*0.3^4=0.2311<BR>\n" );
document.write( "and for 9 is 12C9*0.7^9*0.3^3=0.2397<BR>\n" );
document.write( "The mode is 9.<BR>\n" );
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