2. 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=0.45. Find the probability that at least 10 of the 15 hotel guests were aware of and participated in the hotel’s conservation efforts.
d. Suppose a large hotel chain randomly samples 200 of its guests. The chain’s national director claims that more than 110 of these guests participated in the conservation program. Do you believe this claim? Explain. (HINT: Use the normal approximation to the binomial.)