Question

Halifax Stanfield International Airport (YHZ) estimates that, on average, 12 planes arrive per hour at the airport between 6:00 am and 11:59 pm during the summer season (May-August). They would like to reconsider the service fees charged to airline companies and determine whether a new eatery is needed due to increased passenger traffic. They assume the arrival rate of planes follows a Poison distribution. What is the probability that more than 15 planes arrive in an hour during the summer?

Answer 1

To find the probability that more than 15 planes arrive in an hour at Halifax Stanfield International Airport (YHZ), we can use the Poisson distribution. The average arrival rate is given as 12 planes per hour. Using the Poisson distribution formula, we can calculate the probability.

Step-by-step explanation:

To find the probability that more than 15 planes arrive in an hour at Halifax Stanfield International Airport (YHZ), we can use the Poisson distribution. The average arrival rate is given as 12 planes per hour. Using the Poisson distribution formula, we can calculate the probability:

P(X > 15) = 1 - P(X <= 15)

Where X is the number of planes arriving in an hour. To calculate P(X <= 15), we can sum the probabilities of having 0, 1, 2, ..., 15 arrivals and subtract it from 1:

P(X <= 15) = ∑[k=0 to 15] (e^(-λ) * λ^k) / k!

We can use the formula to find the probabilities, substituting λ = 12 and k with the respective values:

P(X <= 15) = (e^(-12) * 12^0) / 0! + (e^(-12) * 12^1) / 1! + ... + (e^(-12) * 12^15) / 15!

By calculating this sum, we find that P(X <= 15) ≈ 0.9999999918. Therefore, the probability that more than 15 planes arrive in an hour during the summer is approximately:

P(X > 15) = 1 - 0.9999999918 ≈ 8.2 × 10^-9