When a machine is improperly adjusted, it has probability 0.15 ofproducing a defective item. Each day the machine is run until threedefective items are produced. Then it is stopped and checked foradjustment. What is the probability that an improperly adjustedmachine will produce five or more items before being stopped? Whatis the average number of items the machine will produce beforebeing stopped?

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Arnold Odonnell · Accepted Answer

probability of producing a defective item p=0.15 no.of successes r=3 here the no.of defective items follows negativebionomial distribution mean of N.B.D =rqp=3×0.850.15=17 so total no.of items produced =17+3=20 the machine is not adjusted the probability of getting 5 or more defectives with mean no.of defects 20×0.15=3.0 here it follows poison distribution  P(x≥5)=1−F(4)=1−0.815=0.185 average no.of items produced = 20 hope this help you

When a machine is improperly adjusted, it has probability 0.15 ofproducing a defective item. Each day the machine is run until threedefective items ar

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