document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1024839>Question 1024839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Only 35% of the drivers in a particular city wear seat belts. Suppose that 20 drivers are stopped at random what is the probability that exactly four are wearing a seatbelt? (Round your answer to 4 decimal places) </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "Only 35% of the drivers in a particular city wear seat belts. Suppose that 20 drivers are stopped at random what is the probability that exactly four are wearing a seatbelt? (Round your answer to 4 decimal places)<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "Here we have a situation where the probability of a driver wearing seat belts is known and remains constant throughout the experiment of stopping 20 drivers.<BR>\n" );
document.write( "The drivers stopped are assumed to be random and independent.<BR>\n" );
document.write( "These conditions are suitable for modelling using he binomial distribution, where<BR>\n" );
document.write( "P(X=x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Cx%29%2Ap%5Ex%2A%281-p%29%5E%28n-x%29 ALIGN=MIDDLE  ALT=\"C%28n%2Cx%29%2Ap%5Ex%2A%281-p%29%5E%28n-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where n=number of drivers stopped (sample size = 20)<BR>\n" );
document.write( "x=number of drivers wearing seatbelts (4)<BR>\n" );
document.write( "p=probability that a driver wears seatbelts (0.35), and<BR>\n" );
document.write( "C(n,x)=binomial coefficient of x objects chosen from n = n!/(x!(n-x)!)<BR>\n" );
document.write( " <BR>\n" );
document.write( "So the probability of finding 4 drivers wearing seatbelts out of a sample of 20<BR>\n" );
document.write( "P(4;20;0.35)<BR>\n" );
document.write( "=C(20,4)*(0.35)^4*(0.65)^16<BR>\n" );
document.write( "= 4845*0.0150061*0.0010153<BR>\n" );
document.write( "= 0.07382 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );