An advertisement claims that two out of five doctors recommend a certain pharmaceutical product. A random sample of 20 doctors is selected, and it is found that only 2 of them recommend the product.
a. Assuming the advertising claim is true, what is the probability of the observed event?
b. Assuming the claim is true, what is the probability of observing two or fewer successes?
c. Given the sampling results, do you believe the advertisement? Explain.
d. What is the expected number of successes in a sample of 20?