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.
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
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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