1. ## Probability question

Q: A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 24 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted?

A: 0.9307

I'm not sure how to set up the equation to solve it. Any help is appreciated.

2. Use the binomial theorem

$P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$

where n = 24, p= 96/100 (96% = 1 - 4%), k=24 (the entire shipment!)

$P(X=24) = \binom{24}{24}(\tfrac{96}{100})^24(1-\tfrac{96}{100})^{24-24}= \cdots$

3. Sorry but when trying to calculate the above I can't seem to get the answer of 0.9307
Not sure why that is...
Also, how did you get k=24 if the problem says that the shipment is "thousands"?

4. Oops sorry! I prorbably read the question a little too quick! Let me re-think...

5. It's okay, thanks for helping me.

Edit: Maybe there is a mistake? Since the amount is unknown.

,

### a company purchases shipments of machine components and uses this acceptance sampling plan: randomly select and test 21 components and accept the whole batch if there are fewer than 3 defectives. if a particular shipment of thousands of components actuall

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