Question

Suppose small aircraft arrive at a certain airport according to a Poisson process at a rate α=8 per hour.

(a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period? (2 pts)

(b) What are the expected value and standard deviation of the number of small aircraft that arrive during a 90 minute period? (3 pts)

(c) What is the probability that at least 5 aircraft arrive during a 2.5 hour period? (5 pts)

Answer #1

Suppose small aircraft arrive at a certain airport according to
a Poisson process with rate α = 8 per hour, so that the number of
arrivals during a time period of t hours is a Poisson rv with
parameter μ = 8t. (Round your answers to three decimal places.)
(a) What is the probability that exactly 5 small aircraft arrive
during a 1-hour period?
What is the probability that at least 5 small aircraft arrive
during a 1-hour period?
What...

Suppose small aircraft arrive at a certain airport according to
a Poisson process with rate α = 8 per hour, so that the
number of arrivals during a time period of t hours is a
Poisson rv with parameter μ = 8t.
(Round your answers to three decimal places.)
(a) What is the probability that exactly 7 small aircraft arrive
during a 1-hour period?____________
What is the probability that at least 7 small aircraft arrive
during a 1-hour period?_____________
What...

Suppose small aircraft arrive at a certain airport according to
a Poisson process with a mean rate of 8
per hour.
a. Let be the waiting time until the 4th aircraft arrives.
Identify the distribution of T, including any parameters, and
find
P(T ≤ 1)
b. Let Y be the number of aircraft that arrive during a one-half
hour period. Identify the distribution of Y, including any
parameters, and find P(Y ≥ 3)

At an airport domestic flight arrive according to a Poisson
distribution with rate 5 per hour, and international flights arrive
according to a Poisson distribution with rate 1 per hour. What is
the probability that the time between third and fourth flight
arrivals is more than 15 minutes?

Suppose that phone calls arrive at a switchboard according to a
Poisson Process at a rate of 2 calls per minute.
(d)What is the probability that the next call comes in 30
seconds and the second call comes at least 45 seconds after
that?
(e) Let T4 be the time between 1st and 5th calls. What is the
distribution of T4?
(f) What is the probability that the time between 1st and 5th
call is longer than 5 minutes?
Please...

Customers arrive at a bank according to a Poisson process with
rate 10 per hour.
Given that two customers arrived in the ﬁrst 5 minutes, what is
the probability that
(a) both arrived in the ﬁrst 2 minutes.
(b) at least one arrived in the ﬁrst 2 minutes.

Online orders for golf bags arrive to Par Inc. according to a
Poisson process with rate λ=15 bags per hour. Each order
contributes $90 of profit. What is the probability that within the
next thirty minutes Par Inc. will realize at least $720 of profit
contribution due to orders of deluxe golf bags?

Cars arrive at a toll booth according to a Poisson process with
mean 60 cars per hour. If the attendant makes a three minute phone
call, what is the probability that the number of cars passing
through the toll booth during the call is between 2 and 4,
inclusive?

B. Customers arrive at a restaurant according to a Poisson
process. On the average, a customer arrives every half hour.
(a) What is the probability that, 1 hour after opening, there at
least one customer has arrived?
(b) What is the probability that at least 2 customers have
arrived?

Vehicles arrive at a small bridge according to a Poisson process
with arrival rate l = 900 veh/hr. a. What are the mean and the
variance of the number of arrivals during a 30 minutes interval? b.
What is the probability of 0 cars arriving during a 4 second
interval? c. A pedestrian arrives at a crossing point just after a
car passed by. If the pedestrian needs 4 sec to cross the street,
what is the probability that a...

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