Suppose that a large lot of items  is inspected by taking a random sample of size n and  determining the number x of defective items in the  sample. The result is then reported in terms of the  proportion p = x/n of defective items in the sample.  Assume that the binomial distribution can be used to  describe the behavior of the random variable x.   a. Suppose that 5% of the items in a particular lot  are defective and that a random sample of size  n = 5 is to be taken from the lot. Calculate the  probability that the sample proportion p falls  within 1% of the true percent defective in the  lot. That is, find p(0.05- 0.01 <= p <=0.05 + 0.01)  b. Answer the question in part (a) for samples of  size n = 25. c. Answer the question in part (a) for samples of  size n = 100. Hint: Use the normal approximation to the binomial distribution.

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Suppose that a large lot of items  is inspected by taking a random sample of size n and  determining the number x of defective items in the  sample. The result is then reported in terms of the  proportion p = x/n of defective items in the sample.  Assume that the binomial distribution can be used to  describe the behavior of the random variable x.  

a. Suppose that 5% of the items in a particular lot  are defective and that a random sample of size  n = 5 is to be taken from the lot. Calculate the  probability that the sample proportion p falls  within 1% of the true percent defective in the  lot. That is, find p(0.05- 0.01 <= p <=0.05 + 0.01) 

b. Answer the question in part (a) for samples of  size n = 25.

c. Answer the question in part (a) for samples of  size n = 100. Hint: Use the normal approximation to the binomial distribution. 



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