document.write( "Question 1205743: On some busy streets, diamond lanes are reserved for taxis, buses, and cars with three or more passengers. It is estimated that 20% of cars travelling in a certain diamond lane have fewer than three passengers. If 60 cars that travel in a certain diamond lane are selected at random, find the probability that:
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Algebra.Com's Answer #842755 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "On some busy streets, diamond lanes are reserved for taxis, buses, and cars
\n" ); document.write( "with three or more passengers. It is estimated that 20% of cars travelling
\n" ); document.write( "in a certain diamond lane have fewer than three passengers.
\n" ); document.write( "If 60 cars that travel in a certain diamond lane are selected at random, find the probability that:
\n" ); document.write( "(a) fewer than 10 cars have less than 3 passengers.
\n" ); document.write( "(b) at least 15 cars have fewer than 3 passengers.
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document.write( "Obviously, this problem is on the binomial distribution.\r\n" );
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document.write( "The number of trials is n= 60; the probability of the success (fever than 3 passengers) is p= 0.2.\r\n" );
document.write( "The number of success trials k is k<10 in part (a) and k>=15 in part (b).\r\n" );
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document.write( "Since the number of trials, 60, is great, it is recommended to use the normal approximation to \r\n" );
document.write( "the binomial approximation.\r\n" );
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document.write( "In this normal approximation, the mean is mean = np = 60*0.2 = 12; the standard deviation\r\n" );
document.write( "SD =  =  = 3.098386677.\r\n" );
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document.write( "In part (a), you should find a normal distribution probability to get k<10. \r\n" );
document.write( "We can use a regular hand calculator TI-83/84 with standard function normalcfd\r\n" );
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document.write( "                    z1    z2   mean    SD          <<<---===  formatting pattern \r\n" );
document.write( "    P = normalcfd(-9999, 10.5, 12,   3.098386677).                                  (1)\r\n" );
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document.write( "Here 10.5 is the continuity correction factor to the number of 10.\r\n" );
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document.write( "The  ANSWER  (the value of (1)) is the probability  P = 0.3141  (rounded).\r\n" );
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document.write( "Alternatively, to find the value of (1), you may use the online calculator at web-site\r\n" );
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document.write( "https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
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document.write( "It has very convenient simple interface, so even a beginner student can use it without further\r\n" );
document.write( "explanations.  This calculator will produce the same answer (the same value of probability).\r\n" );
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document.write( "Solve part (b) in the same way.  In part (b), use the value of 14.5 as the continuity correction factor for the number 15.\r\n" );
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