Hotels, like airline, often overbook, counting on the fact that some people with reservations will cancel at the last minute. A certain hotel chain finds 20% of the reservations will not be used. Let the Binomial random variable X be the number of reservations canceled. If we randomly selected 15 reservations, what is the probability that more than 8 but less than 12 reservations will be used?

The required probability is 0.334.

Step-by-step explanation:

Since we have given that

N = 15 reservations

probability of reservations will not be used = 0.2

probability of reservations will be used = 1-0.2=0.8

Let X be the Binomial variable,that the number of reservations canceled.

We need to find the probability that more than 8 but less than 12 reservations.

So, it becomes,

Hence, the required probability is 0.334.

Probability that more than 8 but less than 12 reservations will be used is 0.334 .

Step-by-step explanation:

We are given that a certain hotel chain finds 20% of the reservations will not be used which means that 20% of the reservations will be used.

Let X = number of reservations canceled

X ~

The Probability distribution of Binomial distribution is given by;

where, n = number of trials(samples) taken = 15

            r = number of success

            p = probability of success i.e. success of reservations will be used

So, probability that more than 8 but less than 12 reservations will be used is given by = P(X = 9) + P(X = 10) + P(X = 11)

     =

     =

     = 0.043 + 0.103 + 0.188 = 0.334

Therefore, probability that more than 8 but less than 12 reservations will be used is 0.334 .