Delta Airlines' flights from Denver to Dallas are on time $63 \%$ of the time. Suppose fifteen flights are randomly selected, and the number of on-time flights is recorded. Round each answer to at least three decimal places. 1. What is the probability that at least six flights are on time? 2. What is the probability that at most eight flights are on time? 3. What is the probability that fewer than five flights are on time?

Step 1 ：Given that the probability of Delta Airlines' flights from Denver to Dallas being on time is \(p = 0.63\), and we are considering a sample of \(n = 15\) flights.

Step 2 ：We are asked to find the probability that at least six flights are on time. This is equivalent to finding the sum of the probabilities of having 6, 7, ..., 15 flights on time.

Step 3 ：The probability of having \(k\) flights on time is given by the binomial probability formula: \(\binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}\), where \(\binom{n}{k}\) is the number of ways to choose \(k\) successes (on-time flights) out of \(n\) trials (total flights).

Step 4 ：Substituting the given values into the formula, we get the probability of at least six flights being on time as the sum of the probabilities from \(k = 6\) to \(k = 15\).

Step 5 ：Calculating this sum, we find that the probability that at least six flights are on time is approximately \(\boxed{0.981}\).