Television viewers often express doubts about the validity of certain commercials. In an attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 99% confident that their estimate will fall within 2% of the true population proportion?
a) 3989
b) 3967
c) 3963
d) 3982
e) 4000
f) None of the above