A small hotel in a popular resort area has 20 rooms. The hotel manager estimates

Question

A small hotel in a popular resort area has 20 rooms. The hotel manager estimates that 16% of all confirmed reservations are "no-shows." Consequently, the hotel accepts confirmed reservations for as many as 25 rooms. If more confirmed reservations arrive than there are rooms, the overbooked guests are sent to another hotel and given a complementary dinner. Complete parts a through c below assuming that the hotel currently has 25 confirmed reservations. a. Find the probability that no customers will be sent to another hotel. The probability is .3707 (Round to four decimal places as needed.) b. Find the probability that exactly 1 guest will be sent to another hotel The probability is (Round to four decimal places as needed.)

Explanation / Answer

Probability of a guest no-show = 0.16; So the probability of a guest turning up =0.84

Model this as a binomial distribution with probability of success 0.84 and failure 0.16

a. We need the number of guests turning up as less than or equal to 20. This can be found using MS Excel using the formula BINOM.DIST(20,25,0.84,TRUE). The result is 0.3707

b. The probability that exactly 1 guest will be sent to another hotel = probability that 21 guests turn up. This can be found using MS Excel as =BINOM.DIST(21,25,0.84,FALSE). The answer of this is 0.2130.

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