The rates of on-time flights for commercial jets are continuously tracked by the U. S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 2 flights arrive late.

83.29% probability that at least 2 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives late, or it does not arrive late. The probability of a flight arriving late is independent of other flights. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

80 % of its flights arriving on time.

So 100 - 80 = 20% arrive late, which means that

15 Southwest flights

This means that

Find the probability that at least 2 flights arrive late.

Either less than two arrive late, or at least 2 do. The sum of the probabilities of these outcomes is 1. So

We want

Then

In which

So

Then

83.29% probability that at least 2 flights arrive late.

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step-by-step explanatio89