at denver international airport, 84% of recent flights have arrived on time. a sample of 13 flights is studied. find that probability that all 13 flights were on time. round to 4 decimal places

The probability that all 13 flights arrived on time can be calculated using the binomial probability formula, but since we are looking for the case where all flights are on time, we can use a simpler method.

Given that:

- The probability of a flight arriving on time is \( p = 0.84 \)
- The number of flights studied is \( n = 13 \)

The probability that all 13 flights arrive on time is the product of each flight arriving on time, which is calculated as:

\[
P(\text{all on time}) = p^{n} = 0.84^{13}
\]

Now, let's calculate:

\[
P(\text{all on time}) = 0.84^{13} \approx 0.1487
\]

So, the probability that all 13 flights arrived on time is approximately **0.1487** (rounded to 4 decimal places).

Would you like more details or have any further questions?

Here are 5 related questions to expand on this topic:

1. What is the probability that at least one flight out of the 13 is delayed?
2. How would you calculate the probability that exactly 10 out of 13 flights were on time?
3. What is the probability that fewer than 8 flights were on time?
4. How does changing the probability of on-time arrival to 90% affect the result for all 13 flights being on time?
5. How would the probability calculation change if we studied 20 flights instead of 13?

**Tip:** In binomial probability, multiplying individual probabilities assumes independence between events, which is key in many real-world scenarios like flight arrivals.

At Denver International Airport, 84% of recent flights have arrived on time. A sample of 13 flights is studied. Find the probability that all 13 flights were on time. Round to 4 decimal places.

Calculate the probability that all 13 flights arrived on time, given an 84% on-time rate at Denver International Airport. Using the binomial probability formula, learn how to find this probability, including detailed calculations and steps. Suitable for Grades 10-12.

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