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 p5xyn 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(.052.01#p# .051.01)
b. Answer the question in part (a) for samples of
size n 5 25.
c. Answer the question in part (a) for samples of
size n 5 100. Hint: Use the normal approximation
to the binomial distribution.