document.write( "Question 1150678: “Best Fitness” Company is going to hold a stretching class with 15 registered students. From the previous records of stretching classes, the average absence rate per student is 5%.
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\n" ); document.write( "(ii) Given that at least 12 students attend the stretching class, calculate the probability that there will be at most 1 student absent. \n" ); document.write( "
Algebra.Com's Answer #772349 by ikleyn(53937)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            In my solution,  I systematically use the Excel function  ' BINOM.DIST(k, n, p, TRUE/FALSE) '.\r
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\n" ); document.write( "\n" ); document.write( "(i)   Calculate the probability that at most  13  students will attend the stretching class.\r
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document.write( "    P(<= 13 attend) = P(0) + P(1) + P(2) + . . . + P(13) = \"sum%28C%28n%2Ck%29%2A0.95%5E%2815-k%29%2A0.05%5Ek%2C+k=0%2Ck=13%29\" = \r\n" );
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document.write( "                    = cumulative sum = BINOM.DIST(13, 15, 0.95, TRUE) = 0.1710.\r\n" );
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document.write( "    In this part, I confirm the answer by @Boreal.\r\n" );
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\n" ); document.write( "\n" ); document.write( "(ii)   Given that at least  12  students attend the stretching class,  calculate the probability that there will be at most  1  student absent.\r
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document.write( "     \"Given that at least  12  students attend\" means that the given part is\r\n" );
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document.write( "         P(12 attend) + P(13 attend) + P(14 attend) + P(15 attend).\r\n" );
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document.write( "     Next,  \r\n" );
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document.write( "         P(12 attend) = \"C%2812%2C15%29%2A0.95%5E12%2A0.05%5E3\" = BINOM.DIST(12, 15, 0.95, FALSE) = 0.030733;\r\n" );
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document.write( "         P(13 attend) = \"C%2813%2C15%29%2A0.95%5E13%2A0.05%5E2\" = BINOM.DIST(13, 15, 0.95, FALSE) = 0.134752;\r\n" );
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document.write( "         P(14 attend) = \"C%2814%2C15%29%2A0.95%5E14%2A0.05%5E1\" = BINOM.DIST(14, 15, 0.95, FALSE) = 0.365756;\r\n" );
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document.write( "         P(15 attend) = \"C%2815%2C15%29%2A0.95%5E15%2A0.05%5E0\" = BINOM.DIST(15, 15, 0.95, FALSE) = 0.463291.\r\n" );
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document.write( "     Now, they ask to calculate the conditional probability\r\n" );
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document.write( "         P = \"%28P%2814%29+%2B+P%2815%29%29%2F%28P%2812%29+%2B+P%2813%29+%2B+P%2814%29+%2B+P%2815%29%29\" = \"%280.365756+%2B+0.463291%29%2F%280.030733+%2B+0.134752+%2B+0.365756+%2B+0.463291%29\" = \"0.829047%2F0.994533\" = 0.833605.     ANSWER\r\n" );
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document.write( "     In this part, my answer is  different  from that of @Boreal.\r\n" );
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