A public relations agency tells its client that 80% of the residents in a 50-mile radius believe the company is "an industry leader." Skeptical, the company commissions a survey in which just 320 of the 500 persons interviewed felt the company was an industry leader.
If the public relations agency's claim is correct, what is the probability that interviews with 500 people would yield 320 or fewer who felt the company was an industry leader?