Let's go through the parts one by one using the binomial distribution formulas. The binomial distribution is defined by two parameters: $n$, the number of trials, and $p$, the probability of success.

Part 1:

Given that $n = 2525$, so: $n = 2525$ $p = 0.80$, the probability that a flight is on time. Thus: $p = 0.80$

Part 3 (Already answered):

$n = 2525$
$p = 0.80$

Part 4:

Using the binomial distribution formula for exactly $k = 17$ on-time flights: $P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}$ For $n = 2525$, $p = 0.80$, and $k = 17$, the probability is given as $0.0623$.

Part 5 (Interpretation):

In 100 trials of this experiment, the expected number of trials where exactly 17 flights are on time is approximately: $100 \times 0.0623 = 6.23 \approx 6$ So, about 6 out of 100 trials will result in exactly 17 flights being on time.

Part 6:

The probability that fewer than 17 flights are on time is $0.0468$.

Part 7 (Interpretation):

In 100 trials of this experiment, the expected number of trials where fewer than 17 flights are on time is approximately: $100 \times 0.0468 = 4.68 \approx 5$ So, about 5 out of 100 trials will result in fewer than 17 flights being on time.

Part 8:

The probability that at least 17 flights are on time is $0.9532$.

Part 9 (Interpretation):

In 100 trials of this experiment, the expected number of trials where at least 17 flights are on time is approximately: $100 \times 0.9532 = 95.32 \approx 95$ So, about 95 out of 100 trials will result in at least 17 flights being on time.

Part 10:

To find the probability that between 15 and 17 flights (inclusive) are on time, you need to sum the binomial probabilities: $P(15 \leq X \leq 17) = P(X = 15) + P(X = 16) + P(X = 17)$ This requires the binomial distribution formula for each value of $k$ (15, 16, and 17). The resulting probability will then be rounded to four decimal places.

Would you like me to compute the exact value for Part 10 or provide any other details for clarification?

Relative Questions:

1. What is the general formula for the binomial distribution?
2. How do you calculate the probability for exactly $k$ successes in a binomial distribution?
3. How can you interpret a binomial probability in terms of real-world outcomes?
4. What is the difference between "at least" and "fewer than" in probability contexts?
5. How does increasing $n$ affect the shape of the binomial distribution?

Tip: When using the binomial distribution, always ensure that $n$ and $p$ represent clear, countable events and probabilities, such as successes or failures in a fixed number of trials.