Each year, J.D. Power and Associates publishes the results of its North American Hotel Guest Satisfaction Index Study. For 2009, the study revealed that 66% of hotel guests were aware of the hotel's "green" conservation program. Among these guests, 72% actually participated in the program by reusing towels and bed linens. In a random sample of 15 hotel guests, consider the number (x) of guests who were aware of and participated in the hotel's conservation efforts.
a. Explain why x is (approximately) a binomial random variable.
b. Use the rules of probability to determine the value of p for this binomial experiment.
c. Assume p = .45. Find the probability that at least 10 of the 15 hotel guests were aware of and participated in the hotel's conservation efforts.