# Question: A commuter airline deliberately overbooks fights figuring that only 75

A commuter airline deliberately overbooks fights, figuring that only 75% of passengers with reservations show up for its fights. It files small propeller planes that carry 20 passengers.

(a) In order to use a binomial model in this problem, what assumptions are necessary? Are these reasonable?

(b) If the airline allows 25 passengers to book reservations for a fight, what is the probability that the fight will be oversold? Do not use the probability distribution and instead think about the mean and shape of the binomial distribution.

(c) Find the probability of overbooking. Did the rough approach taken in part (b) get close enough to the right answer?

(a) In order to use a binomial model in this problem, what assumptions are necessary? Are these reasonable?

(b) If the airline allows 25 passengers to book reservations for a fight, what is the probability that the fight will be oversold? Do not use the probability distribution and instead think about the mean and shape of the binomial distribution.

(c) Find the probability of overbooking. Did the rough approach taken in part (b) get close enough to the right answer?

**View Solution:**## Answer to relevant Questions

Every now and then even a good diamond cutter has a problem and the diamond breaks. For one cutter, the rate of breaks is 0.1%. (a) What probability model seems well suited to this problem? Why? (b) If this cutter works on ...Historically a bank expects about 5% of its borrowers to default (not repay). The bank currently has 250 loans outstanding. (a) In order to use a binomial model to compute the probabilities associated with defaults, what ...1. Mean of X 2. Variance of X 3. Probability of X being less than its mean 4. Probability of X being less than μ + σ 5. Standard deviation of Z 6. Probability that a z-score based on X is less than 1 in magnitude 7. ...The normal quantile plot of daily stock returns for General Motors during 1992–1993 (507 trading days) shows an anomaly, a flat spot at zero. (a) What’s happened? (b) Why does the anomaly not appear in the histogram? Using the normal table in the back of the book or software, find the value of z that makes the following probabilities true. You might find it helpful to draw a picture to check your answers. (a) P (Z < z) = 0.20 (b) P (Z ...Post your question