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# 5. (3 + 3 points) During a quality check on a batch of mobile phones, a double is performed sampling plan as follows. First; a sample of 50 mobile phones is randoml...

## Question

###### 5. (3 + 3 points) During a quality check on a batch of mobile phones, a double is performed sampling plan as follows. First; a sample of 50 mobile phones is randomly selected. lemons for control. If all of these are correct (not defective) , the party is accepted, but if more than or equal t0 two are defective, the Iot is rejected. If exactly one is defective, proceed to a second selection where another 50 mobile phones are checked: If all of these are correct, the party is accepted, otherwise r

5. (3 + 3 points) During a quality check on a batch of mobile phones, a double is performed sampling plan as follows. First; a sample of 50 mobile phones is randomly selected. lemons for control. If all of these are correct (not defective) , the party is accepted, but if more than or equal t0 two are defective, the Iot is rejected. If exactly one is defective, proceed to a second selection where another 50 mobile phones are checked: If all of these are correct, the party is accepted, otherwise rejected the. Assume that the error rate in the batch is p 2% defective (a) Assume that the batch is very large so that the sample sizes are negligible compared to with the size of the party. Calculate the probability that the party will be accepted. (b) Assume now instead that the size of the lot is 300. Give an exact expression of the probability that the party is accepted. The term is allowed t0 contain binomial coefficients which does not need to be calculated.

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