You are investigating the punctuality of the airlines in Asia. Your survey tells

Question

You are investigating the punctuality of the airlines in Asia. Your survey tells you that, out of 15 airlines, 80% of them are likely to be late at least once a month. As- sume the punctuality random variable follows a bino- mial distribution. Determine the following. a. Which assumptions do you need to make in order to be correct in considering a binomial distribution for your variable? b. How many airlines will be late in one month? c. What is the standard deviation of this random variable (i.e., the risk of being late)? d. What is the probability that they all will be late? untr a new pro-

Explanation / Answer

Total number of airlines n = 15

Here Pr(airline will be late once month) = 0.80

1.Each replication of the process results in one of two possible outcomes

2. The probability of success is the same for each replication

3. The replications are independent, meaning here that a success in one patient does not influence the probability of success in another

Here parameter n = 15 and p = 0.8

b. Number of airlines will be late in one month = 15 * 0.80 = 12

c. standard deviation of this random variable = sqrt[p * (1-p) * N] = sqrt [0.2 * 0.8 * 15] = 1.5492

d. Pr(All will be late) = Pr ( X = 15) = 15C15 (0.8)15 = 0.0352

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