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**Hashem** Dear all,

I have stumbled upon this impossible question from my teacher. The question is a binomial distribution and is as follows:

**. A bakery supplies batches of jam doughnuts for a local supermarket. Batches are either high-quality or low-quality. 1% of doughnuts in high-quality batches have no jam. 10% of doughnuts in low-quality batches have no jam. To try to intercept low-quality batches, the supermarket takes a sample of 50 doughnuts from each batch and tests them. If two or more doughnuts are found to have no jam, the batch is rejected.**

(a) Explain what a Type I error and Type II error would be in this case.

(b) Calculate the probability of each type of error.

*Hint: use the binomial distribution: pr(r) = NCr **p**r**(1-**p**)N-r where r is the number of times a particular outcome occurs in N trials and **p** is the probability of that outcome occurring in 1 trial*

(c) Calculate the power of the test.

(d) The supermarket can alter the error probabilities by changing the sample size or by changing the rejection criteria. What would you recommend if: (i) doughnuts without jam are found to affect consumer safety? (ii) there is no alternative bakery that could supply doughnuts?

Now I can easily solve for (a), but (b) is just killing me, I always end up with 0.006% from (0.99^48 * 0.01 *0.01), the teacher hinted 8% at me but she did not confirm it and I may just have heard her wrong. I cant really solve this question and its killing me!!!

Help me Please!!!