document.write( "Question 1139701: The median life of Brand LT5 batteries is 100 hours. What is the probability that in a set of three such batteries, exactly two will last longer than 100 hours? \n" ); document.write( "

Algebra.Com's Answer #760206 by ikleyn(52851) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "        I just saw (and solved) several similar problems in this forum.\r
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\n" ); document.write( "\n" ); document.write( "        They are not exactly and precisely mathematical, since the condition is not completed and requires some additions.\r
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\n" ); document.write( "\n" ); document.write( "        Again, they are not exactly and precisely mathematical, but mostly serve to exercise your \"common sense\".\r
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\n" ); document.write( "\n" ); document.write( "        They require you to reformulate the condition in a way the problem to obtain its sense.\r
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\n" ); document.write( "\n" ); document.write( "        And they require such an addition \r
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document.write( "           a)  \"to be consistent\"  with the given part,  and  \r\n" );
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document.write( "           b)  to be likelihood.\r\n" );
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\n" ); document.write( "\n" ); document.write( "        So, again, it is not \"the pure Mathematics in its pure instance\" - it is the common sense hypothesizing
\n" ); document.write( "        to make right formulation and to get the problem solved     ( = to get a likelihood solution ).\r
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\n" ); document.write( "\n" ); document.write( "        After this introduction, I can now move to the solution.\r
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document.write( "Having nothing else given, an appropriate hypothesis is to assume that we have continuous random variable \r\n" );
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document.write( "    X = \"the time of a battery service / (or \"life\")\" \r\n" );
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document.write( "with random values that are uniformly distributed with the minimum value of 0 and the maximum value of 200 hours.\r\n" );
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document.write( "Then the mean average  is exactly 100, as the problem states, and  the condition becomes \"consistent with the given part\" and \"self-closed\".\r\n" );
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document.write( "Then the probability  P(X < 100) = , as well as  P(x > 100) = .\r\n" );
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document.write( "Therefore, the probability that exactly two of the three batteries will last longer than 100 hours is   = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Unusual probability problems \r
\n" ); document.write( "\n" ); document.write( "in this site, where you will find many other similar problems solved and explained.\r
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\n" ); document.write( "\n" ); document.write( "WARNING ! : When I posted similar solution to a similar problem to one of the visitors of this forum,\r
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\n" ); document.write( "\n" ); document.write( "he (or she) posted me back \"the empty line response\", expressing his (or her) dissatisfaction,\r
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\n" ); document.write( "\n" ); document.write( "and I momentarily got understanding that this person is an idiot.\r
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\n" ); document.write( "\n" ); document.write( "So, carrying about your reputation, please do not repeat this stupid action, because right now you got
\n" ); document.write( "a BRILLIANT SOLUTION with a BRILLIANT EXPLANATION.\r
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