Question

Delta Airlines' flights from Chicago to Seattle are on time 80 % of the time. Suppose 8 flights are randomly selected, and the number on-time flights is recorded. Round answers to 3 significant figures The probability that exactly 5 flights are on time is = The probability that at most 4 flights are on time is = | The probability that at least 3 flights are on time is =|

Answer 1

To find the desired probabilities, we apply the binomial probability formula with n = 8 trials (flights) and a success probability of 0.8 (on-time flight). Exact, at most, and at least scenarios are calculated by summing the appropriate individual probabilities.

Step-by-step explanation:

The student's question involves calculating probabilities for a given number of on-time flights by Delta Airlines from Chicago to Seattle. This problem can be approached using the binomial probability formula:

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

Where P(X = k) is the probability of k successes in n trials, nCk is the combination of n items taken k at a time, p is the probability of success, and (1 - p) is the probability of failure.

To calculate the probabilities:

1. Exactly 5 flights are on time: Since the probability of an on-time flight is 80% (or 0.8), we use k = 5 and n = 8 to calculate P(X = 5).
2. At most 4 flights are on time: We need to sum the probabilities of 0, 1, 2, 3, and 4 flights being on time.
3. At least 3 flights are on time: We calculate this by summing the probabilities from 3 flights to 8 flights being on time, or subtracting the cumulative probability of 0, 1, and 2 flights being on time from 1.