document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168965>Question 1168965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From experience, an airline knows that only 73 percent of the passengers booked on a flight from New York to Los Angeles actually board their flight. If this percentage is correct, what is the probability that, in a random sample of 6 booked passengers from New York to Los Angeles, exactly 3 show up?<BR>\n" );
document.write( "Round your answer to three decimal places. </SPAN>\n" );
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document.write( "p = probability of success<BR>\n" );
document.write( "p = probability someone showing up (ie actually boarding their flight)<BR>\n" );
document.write( "p = 0.73\r<BR>\n" );
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document.write( "n = sample size<BR>\n" );
document.write( "n = 6\r<BR>\n" );
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document.write( "x = number of people who show up (out of n = 6 people)<BR>\n" );
document.write( "x = 3\r<BR>\n" );
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document.write( "We'll use the binomial probability distribution formula below<BR>\n" );
document.write( "B(x) = (n C x)*(p^x)*(1-p)^(n-x)<BR>\n" );
document.write( "B(3) = (6 C 3)*(0.73^3)*(1-0.73)^(6-3)<BR>\n" );
document.write( "B(3) = 20*(0.73^3)*(0.27^3)<BR>\n" );
document.write( "B(3) = 20*(0.73^3)*(0.27^3)<BR>\n" );
document.write( "B(3) = 20*0.389017*0.019683<BR>\n" );
document.write( "B(3) = 20*0.007657021611<BR>\n" );
document.write( "B(3) = 0.15314043222<BR>\n" );
document.write( "B(3) = 0.153<BR>\n" );
document.write( "In a sample of 6 people, there's roughly a 15.3% chance of exactly 3 showing up and actually boarding their flight.\r<BR>\n" );
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document.write( "Note: The notation 6 C 3 refers to the nCr combination notation. You'll use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nCr+=+%28n%21%29%2F%28r%21%2A%28n-r%29%21%29 ALIGN=MIDDLE  ALT=\"nCr+=+%28n%21%29%2F%28r%21%2A%28n-r%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or you can use Pascals Triangle. \r<BR>\n" );
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document.write( "Final Answer: 0.153\r<BR>\n" );
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