document.write( "Question 938768: It is thought that, on average, 3% of light bulbs produced by a certain company last for less than 250 hours. This will be referred to as being defective.
\n" ); document.write( "In an inspection scheme, a sample of 25 light bulbs is selected at random from a large batch, they are tested for 250 hours and the number of defective bulbs is noted.
\n" ); document.write( "If the number is more than two, the whole batch is rejected; if it is less than two, the whole batch is accepted.
\n" ); document.write( "If there are exactly two defective bulbs in this batch, a further sample of size ten is taken.
\n" ); document.write( "The whole batch is rejected if there are any defective bulbs in this sample; otherwise the batch is accepted.
\n" ); document.write( "Find
\n" ); document.write( "(i)the probability that the batch is accepted after taking the first sample
\n" ); document.write( "(ii)the probability that the batch is accepted after taking the second sample
\n" ); document.write( "(iii)the probability that the batch is rejected. \n" ); document.write( "

Algebra.Com's Answer #571943 by ewatrrr(24785) $\"\"$ $\"About$

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p(def) = .03, n = 25
\n" ); document.write( "i) P(accepted) = P(x < 2) = binomcdf(25, .03,1)
\n" ); document.write( "...
\n" ); document.write( "ii) P ( batch is accepted after taking the second sample)
\n" ); document.write( "P = [binompdf(25, .03,2)][10^(.97)]
\n" ); document.write( "...
\n" ); document.write( "iii) P(probability that the batch is rejected)
\n" ); document.write( "P = [1-binomcdf(25, .03, 2] + [1 - [binompdf(25, .03,2)][10^(.97)] \n" ); document.write( "

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