Problem 48E

Hotel guest satisfaction. 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 participate in the program by reusing towels and bed linens. In a random sample of 15 hotel guests, consider the number (x) of guests who are aware and participate 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 are aware of and participate in the hotel’s conservation efforts.

Solution :

Step 1 of 3:

Given a random sample N = 15.

a). To explain why x is a binomial random variable.

If x is approximately a binomial random variable, the characteristics is

- n identical trials. Although the trials are not exactly identical, they are close. Taking a sample of size n = 15 from a very large population will result in trials being essentially identical.
- Two possible outcomes. S = hotel guest is aware of and participates in conservation efforts and F = hotel guest is not aware of and/or does not participates in conservation efforts.
- P(S) remains the same from trial to trial.
- Trials are independent.
- The random variable x = number of hotel guests who are aware of and participate in conservation efforts in n = 15 trials.

Therefore x is very close to binomial distribution. So x is a binomial distribution.