Question

The US Bureau of Transportation Statistics reports that, of all domestic flights, from June 2003 to December 2022, 78.73% were on time. Suppose that this is the proportion of US domestic flights that arrive on time.

Are you (and a few other American people) going to fly back home for Thanksgiving? Out of a simple random sample of 120 domestic flights scheduled next week, what is the probability that at least 102 will land on time. Make sure to identify the sampling distribution you use and check all necessary assumptions/conditions.

Answer 1

The probability of at least 102 flights out of 120 landing on time is approximately 88.09%.

Step-by-step explanation:

To calculate the probability that at least 102 out of 120 flights will land on time, we need to use the binomial distribution. Let's assume that each flight has a probability of 78.73% of landing on time, which is the proportion reported by the US Bureau of Transportation Statistics.

The probability of exactly k successes in n trials, where the probability of success in each trial is p, can be calculated using the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

In this case, we want to find the probability of at least 102 successful flights out of 120, so we need to calculate the probabilities for k = 102, 103, 104, ..., 120 and sum them up.

Using a binomial probability calculator or software, we can find that the probability of at least 102 successful flights out of 120 is approximately 0.8809, or 88.09%.