Question

Vehicles arrive at the Bun-and-Run drive-thru at a Poisson rate of 10 per hour. On average, 25% of these vehicles are trucks. Calculate the probability that at least 2 trucks arrive between noon and 2:00 PM. (Round to 3 decimals)

Answer #1

At a border inspection station, vehicles arrive at the rate of 8
per hour in a Poisson distribution. For simplicity in this problem,
assume that there is only one lane and one inspector, who can
inspect vehicles at the rate of 15 per hour in an exponentially
distributed fashion.
a. What is the average length of the waiting line?
(Round your answer to 2 decimal places.)
b. What is the average total time it takes for
a vehicle to get...

Suppose that Airplanes are coming into an Airfield at an average
rate 4 per hour according to a Poisson process. We start to account
the Airplanes from 3:00 (pm).
(a) What is the probability that the third Airplanes takes more
that 2 hours to arrive?
(b) What is the expected time the third Airplanes arrive to the
station?
(c) What is the probability that three Airplanes arrive between
3:00pm-4:00pm?
(d) What is the probability that no buses arrive between
3:00pm-5:00pm?

Suppose that buses are coming into a station at an average rate
4 per hour according to a Poisson process. We start to account the
buses from 1:00 (pm).
(a) What is the probability that no buses arrive between
1:00pm-2:00pm?
(b) What is the probability that three buses arrive between
1:00pm-3:00pm?
(c) What is the probability that the third bus takes more that 3
hours to arrive?
(d) What is the expected time the third bus arrive to the
station?

At a 24-hour computer repair facility broken-down computers
arrive at an average rate of 3 per day, Poisson distributed.
What is the probability that on a given day no computers arrive
for repair?
What is the probability that on a given day at least 3
computers arrive for repair?
What is the distribution of the time between arrivals of
computers to this facility and what is the average time between
arrivals?
On one particular day no computer has arrived for...

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.

Visitors arrive to an internet site according to a Poisson
process with an average of 10 visitors per hour. Use this
information to answer the following questions.
1.What is the probability that 12 visitors arrive in an hour?
(Use 4 decimal places)
2. What is the probability that at least 20 minutes elapse
between visitors to the website? (Use 4 decimal places)
3.What is the probability that at least 2 visitors come to the
website in 30 minutes? (Use 4...

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 customers arrive at a bank at a rate of 10 per
hour. Assume that the number of customer arrivals X follows a
Poisson distribution.
1. Find the probability of more than 25 people arriving within
the next two hours using the Poisson mass function.
2. Find the probability of more than 25 people arriving within
the next two hours using the normal approximation to the
Poisson.
3. Compute the percent relative difference between the exact
probability computed in...

A grocery store counts the number of customers who arrive during
an hour. The average over a year is 20 customers per hour. Assume
the arrival of customers follows a Poisson distribution. (It
usually does.)
Find the probability that at least one customer arrives in a
particular one minute period. Round your answer to 3
decimals.
Find the probability that at least two customers arrive in a
particular 4 minute period. Round your answer to four decimals.

Suppose that customers arrive at a bank at a rate of 10 per
hour. Assume that the number of customer arrivals X follows a
Poisson distribution.
Find the probability of more than 25 people arriving within the
next two hours using the Poisson mass function.
Find the probability of more than 25 people arriving within the
next two hours using the normal approximation to the Poisson.
Compute the percent relative difference between the exact
probability computed in part 1 and...

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