document.write( "Question 1205742: On some busy streets, diamond lanes are reserved for taxis, buses, and cars with three or more passengers.
\n" ); document.write( "It is estimated that 20% of cars travelling in a certain diamond lane have fewer than three passengers.
\n" ); document.write( "a. Is the variable in the question discrete or random? Justify your answer.
\n" ); document.write( "If 60 cars that travel in a certain diamond lane are selected at random, find the probability that:
\n" ); document.write( "b. exactly 10 cars have less than 3 passengers. \n" ); document.write( "

Algebra.Com's Answer #842756 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( "exactly 10 cars have less 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.\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 this problem, 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(9.5, 10.5, 12,   3.098386677).                                  (1)\r\n" );
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document.write( "Here 9.5, 10.5 are the continuity correction factors to the number of 10.\r\n" );
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document.write( "The  ANSWER  (the value of (1)) is the probability  P = 0.1043  (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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