An advertising agency conducted an ad campaign aimed at making consumers in an Eastern state aware of a new product. Upon completion of the campaign, the agency claimed that 20 percent of consumers in the state had become aware of the product. The product's distributor surveyed 1,000 consumers in the state and found that 150 were aware of the product.
a. Assuming that the ad agency's claim is true:
(1) Verify that we may use the normal approximation to the binomial.
(2) Calculate the mean, μ, and the standard deviation, σ, we should use in the normal approximation.
(3) Find the probability that 150 or fewer consumers in a random sample of 1.000 consumers would be aware of the product.
b. Should the distributor believe the ad agency's claim? Explain.