Question 3: Air traffic control is essential for the safe landing and departure

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Question 3: Air traffic control is essential for the safe landing and departure of plans. You are monitoring a particular airport, and observe that the arrival rate of small planes 6 per hour according to a Poisson distribution. Use this information and answer questions 3a to 3e. Question 9 5 pts Question 3a You are interested in to know how many small planes arrive within a one-hour period. What is the random variable? () x-number of small planes that arrive in a day X number of small planes that arrive in an hour X-number of small planes that arrive x-number of small planes that arrive in a week DQuestion 10 6 pts Question 3b: You decided to spend an hour to observe how many planes arrive. What is the probability that you observe exactly 6 small planes arrival? (use 3 decimal places) Question 11 7 pts Question 3c On average, how many small planes would you expect to observe during an 8-hour Question 12 7 pts Question 3d: What is the probability that you observed at least 3 arrivals of small planes in the first 30 minutes of your observation? (use 3 decimal places) Question 13 7 pts Question 3e You have observed 5 arrivals of small planes in the first 40 minutes of your observation. What is the probability that you observe a total of 6 small plane arrivals in the one-hour observation? luse 3 decimall places)

Explanation / Answer

Given that arrival rate of small planes is 6 per hour and it follows Poisson distribution.

3a) R. v is X : Number of small planes arrive in one hour period

3b) Probability of observing exactly 6 planes in one hour period = P[X=6] = 0.160623

3c) On an average expected number of small planes in 8 hour period = 6 * 8 = 48

3d) Probability of observing at least three arrivals in first 30 minutes = Probability of X > 2 with model parameter = 6/2 = 3 = P[X > 2|=3] = 0.57681

3e) If 5 small planes are arrived in first 40 minutes, probability that in 20 minutes 1 small plane will arrive = P[X=1|=2] = 0.270671

Here for 60 minutes 6 small planes arrive and therefor for fraction of hours the necessary calculations are used as a model parameter.

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