Hotel guest satisfaction. Each year, J. D. Power and Associates publishes the re

ID: 3371366 • Letter: H

Question

Hotel guest satisfaction. Each year, J. D. Power and Associates publishes the results of its North American Hotel Guest Satisfaction Index Study. For 2015, the study revealed that 15% of hotel guests were "delighted" with their experience (giving a rating of 10 out of 10). Among these guests, 80% stated they would "definitely” recom- mend the hotel. In a random sample of 15 hotel guests, consider the number (x) of guests who were delighted with their stay and would recommend the hotel. a. Explain why x is (approximately) a binomial random variable. - Use the rules of probability to determine the value of 10. Find the probability that at least 10 of for this binomial experiment. c. Assume p = .10. Find the probability that a hotel guests were delighted with their stay and the 15 hotel guests were delighted would recommend the hotel.

Explanation / Answer

Result:

a).

For the binomial distribution we need fixed number of trials and each trial has two possible outcomes, success or failure. The probability of success, p, is the same for each trial and each trial is independent.

In this case we are having fixed number is 15 and event is delighted and recommended or not. This probability is fixed and therefore this is binomial.

b).

probability of delighted = 0.15

P( recommended/ delighted) = 0.80

P(delighted and recommended) = 0.80*0.15 =0.12

c).

n=15, p=0.10

Binomial Probabilities Table

P(X)

0.20589113

0.34315189

0.26689591

0.12850544

0.04283515

0.01047081

0.00193904

0.00027701

0.00003078

0.00000266

0.00000018

0.00000001

0.00000000

P( x ? 10) = 0.00000018+0.00000001+0+0+0+0

=0.00000019