document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096463>Question 1096463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the answer for : <BR>\n" );
document.write( "For drivers aged 20-24 there is a 34% chance of having a car accident in a one year period (based on data from the National Safety Council). In a sample of 12 drivers aged 20-24, let X be the number who have had an accident in the last year. Consider the following probability distribution for X.  Find P(x), when x = 5 \r<BR>\n" );
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document.write( "Given table <BR>\n" );
document.write( "x        P(x)<BR>\n" );
document.write( "6      0.1180<BR>\n" );
document.write( "7	0.0521<BR>\n" );
document.write( "8	0.0168<BR>\n" );
document.write( "9	0.0038<BR>\n" );
document.write( "10	0.0006<BR>\n" );
document.write( "11	0.0001<BR>\n" );
document.write( "12	0.0000<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 #710936 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=710936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "This is a binomial probability distribution problem.\r<BR>\n" );
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document.write( "The sample size is n = 12 and we want k = 5 to be the number of people who had an accident.\r<BR>\n" );
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document.write( "The probability of getting into an accident, for any given independent trial, is p = 0.34 (34% = 34/100 = 0.34)\r<BR>\n" );
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document.write( "Compute the combination value below<BR>\n" );
document.write( "n C k = (n!)/(k!*(n-k)!)<BR>\n" );
document.write( "12 C 5 = (12!)/(5!*(12-5)!)<BR>\n" );
document.write( "12 C 5 = (12!)/(5!*7!)<BR>\n" );
document.write( "12 C 5 = (12*11*10*9*8*7!)/(5!*7!)<BR>\n" );
document.write( "12 C 5 = (12*11*10*9*8)/(5!)<BR>\n" );
document.write( "12 C 5 = (12*11*10*9*8)/(5*4*3*2*1)<BR>\n" );
document.write( "12 C 5 = 95040/120<BR>\n" );
document.write( "12 C 5 = 792\r<BR>\n" );
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document.write( "Use that result to compute the binomial distribution value<BR>\n" );
document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "P(X = 5) = (12 C 5)*(0.34)^(5)*(1-0.34)^(12-5)<BR>\n" );
document.write( "P(X = 5) = (12 C 5)*(0.34)^(5)*(0.66)^(7)<BR>\n" );
document.write( "P(X = 5) = (792)*(0.34)^(5)*(0.66)^7<BR>\n" );
document.write( "P(X = 5) = (792)*(0.0045435424)*(0.05455160701056)<BR>\n" );
document.write( "P(X = 5) = 0.196303171236968\r<BR>\n" );
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document.write( "Rounding to four decimal places, we get the final answer of <font color=red size=4>0.1963</font> (this answer is approximate)\r<BR>\n" );
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document.write( "This means that if we selected 12 people, then the chances that exactly five of them got into an accident last year is roughly 0.1963\r<BR>\n" );
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document.write( "Note: 0.1963 is equivalent to 19.63%<BR>\n" );
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