document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190363>Question 1190363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Driving to Work Alone: It is reported that 77% of workers aged 16 and over drive to work alone.<BR>\n" );
document.write( "Choose 8 workers at random.<BR>\n" );
document.write( "Please, find the probability that<BR>\n" );
document.write( "a) All drive to work alone<BR>\n" );
document.write( "b) More than one-half drive to work alone<BR>\n" );
document.write( "c) Exactly 3 drive to work alone<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 #822002 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "n = 8 = sample size<BR>\n" );
document.write( "p = 0.77 = probability of success (i.e. picking someone who drives alone)<BR>\n" );
document.write( "x = number of drivers who are alone<BR>\n" );
document.write( "x takes on the integer values from the set {1,2,...,7,8}\r<BR>\n" );
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document.write( "For this part, we'll only worry about x = 8 which is involving everyone sampled driving alone.\r<BR>\n" );
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document.write( "B(x) = binomial distribution value<BR>\n" );
document.write( "B(x) = (nCx)*(p)^x*(1-p)^(n-x)<BR>\n" );
document.write( "B(8) = (8C8)*(0.77)^8*(1-0.77)^(8-8)<BR>\n" );
document.write( "B(8) = 0.123574<BR>\n" );
document.write( "The nCx refers to the nCr combination formula\r<BR>\n" );
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document.write( "Answer: Approximately 0.123574\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "n = 8 cuts in half to 4<BR>\n" );
document.write( "\"more than half\" means \"more than 4\"\r<BR>\n" );
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document.write( "We'll need to compute each B(x) value for x = 5, 6, 7 and 8.<BR>\n" );
document.write( "The steps are similar to the previous part. \r<BR>\n" );
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document.write( "You should find that<BR>\n" );
document.write( "B(5) = 0.184 427<BR>\n" );
document.write( "B(6) = 0.308 715 <BR>\n" );
document.write( "B(7) = 0.295 293<BR>\n" );
document.write( "B(8) = 0.123 574<BR>\n" );
document.write( "all of which are approximate.\r<BR>\n" );
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document.write( "Those values add up to 0.912 009\r<BR>\n" );
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document.write( "Answer: 0.912009 approximately\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "Plug in x = 3 to get...<BR>\n" );
document.write( "B(x) = (nCx)*(p)^x*(1-p)^(n-x)<BR>\n" );
document.write( "B(3) = (8C3)*(0.77)^3*(1-0.77)^(8-3)<BR>\n" );
document.write( "B(3) = 0.016 455\r<BR>\n" );
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document.write( "Answer: 0.016455\r<BR>\n" );
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document.write( "All results are approximate rounded to 6 decimal places.<BR>\n" );
document.write( "Round however else you need if your teacher instructs it.<BR>\n" );
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