A small hotel in a popular resort area has 2020 rooms. The hotel manager estimat

Question

A small hotel in a popular resort area has

2020

rooms. The hotel manager estimates that

1414%

of all confirmed reservations are "no-shows." Consequently, the hotel accepts confirmed reservations for as many as

2525

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

2525

confirmed reservations.

a. nbspa. Find

the probability that no customers will be sent to another hotel.

Explanation / Answer

Let X be a random variable denoting no show of customer

given n=2525 confirmed reservations

probability of no show (p)=0.1414  

q=1-p =0.8586

So X~ Binomial(n,p)

P(no customers will be sent to another hotel) = P(X=2525-2020)=P(X=505)

P(X=505)= 2525C505 (0.1414)^505 (0.8586)^2020

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