# An airport limousine can accommodate up to four passengers on any one trip. The company will...

## Question:

An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation to get on board. From previous experience, 20% of those making reservations do not appear for the trip. Supposing that six reservations are made, answer the following questions and show work.

(1) Let X be the number of customers that actually appear for the trip. What distribution does X follow? State the family of probability distribution, and the parameter(s).

(2) What is the probability that at least one individual with a reservation cannot be accommodated on the trip?

(3) What are the expected value and the variance of X?

## Solving Binomial probabilities:

Binomial probability is the probability of getting {eq}x {/eq} successes in {eq}n {/eq} independent trials of with two possible outcomes, success or failure known as a binomial experiment. probability is given by the formula;{eq}P(X=x) ={n \choose x} \times p^x \times (1-p)^{n-x}\space, x=0,1,2,3,...,n {/eq}, where {eq}x {/eq} is the number of successes and {eq}p {/eq} is the probability of success.

1.

We are given that X is the number of customers that actually appear for the trip.

X follows binomial distribution with n = 6 and p = 1 -0.2 =...

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