Refer to the 2015 North American Hotel Guest Satisfaction Index Study, Exercise 4.49. You determined that the probability that a hotel guest was delighted with his or her stay and would recommend the hotel is .12. Suppose a large hotel chain randomly samples 200 of its guests. The chain's national director claims that more than 50 of these guests were delighted with their stay and would recommend the hotel.

a. Under what scenario is the claim likely to be false?

b. Under what scenario is the claim likely to be true?