Please help, probability double sampling scheme

statrwe

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Nov 24, 2012
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Please help with a hint of doing his question, I have drawn the diagram but still confused.


Q)In a food production process, packaged items are sampled as they come off a
production line. A random sample of 5 items from each large production batch is
checked to see whether each item is tightly packed. A batch will be accepted
immediately if all of these 5 items are tightly packed, and rejected immediately if at
least 3 items among the 5 are not tightly packed. Otherwise a second sample is taken
before making a decision.
Suppose that 80% of the items produced by the machine are tightly packed

a)When a second sample is to be taken, it also consists of 5 items. What is the
probability that in a combined sample of 10 items there are at least 8 tightly
packed?

Thanks.
 
Please help with a hint of doing his question, I have drawn the diagram but still confused.


Q)In a food production process, packaged items are sampled as they come off a
production line. A random sample of 5 items from each large production batch is
checked to see whether each item is tightly packed. A batch will be accepted
immediately if all of these 5 items are tightly packed, and rejected immediately if at
least 3 items among the 5 are not tightly packed. Otherwise a second sample is taken
before making a decision.
Suppose that 80% of the items produced by the machine are tightly packed

a)When a second sample is to be taken, it also consists of 5 items. What is the
probability that in a combined sample of 10 items there are at least 8 tightly
packed?

Thanks.
What is the probability that in a combined sample of 10 items - all ten are tightly packed?

What is the probability that in a combined sample of 10 items - only nine are tightly packed?

What is the probability that in a combined sample of 10 items - only eight are tightly packed?
Now,
What is the probability that in a combined sample of 10 items there are at least 8 tightly packed?


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We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

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Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.
 
Please help with a hint of doing his question, I have drawn the diagram but still confused.


Q)In a food production process, packaged items are sampled as they come off a
production line. A random sample of 5 items from each large production batch is
checked to see whether each item is tightly packed. A batch will be accepted
immediately if all of these 5 items are tightly packed, and rejected immediately if at
least 3 items among the 5 are not tightly packed. Otherwise a second sample is taken
before making a decision.
Suppose that 80% of the items produced by the machine are tightly packed

a)When a second sample is to be taken, it also consists of 5 items. What is the
probability that in a combined sample of 10 items there are at least 8 tightly
packed?

Thanks.

Okay my thoughts about the answer are as follows.
For a second sample to be taken, there must be 0 or 1 or 2 tightly packed so to get a total of 8 tightly packed from the first and second selections, we need to add up binomial probabilities.

1) x =0 from n1 and x=8 from n2
2) x=1 from n1 and x=7 from n2
3) x=2 from n1 and x=6 from n2

For each case use binomial B(5, 0.8), where B(n,p). where p =0.8

What do you think about this approach, is it right?
 
Okay my thoughts about the answer are as follows.
For a second sample to be taken, there must be 0 or 1 or 2 tightly packed so to get a total of 8 tightly packed from the first and second selections, we need to add up binomial probabilities.

1) x =0 from n1 and x=8 from n2
2) x=1 from n1 and x=7 from n2
3) x=2 from n1 and x=6 from n2

For each case use binomial B(5, 0.8), where B(n,p). where p =0.8

What do you think about this approach, is it right?
 
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