Question

In: Civil Engineering

1.At a road section, an average of 15 vehicles arrive during a 10-minute interval. If vehicles...

1.At a road section, an average of 15 vehicles arrive during a 10-minute interval. If vehicles arrive according to a Poisson distribution, what is the probability that the number of vehicles ­arriving during a 3-minute interval is between 2 and 5 (i.e., 2 ≤ k ≤ 5)?

a.0.110

b.0.171

c.0.642

d.0.653

e.0.703

2.At a specific point on a highway, it is known that the time headways between successive vehicles are exponentially distributed and that 65% of the headways are greater than 3 seconds. What is the probability that less than two vehicles arrive during a 20-second interval?

a.0.219

b.0.233

c.0.350

d.0.397

e.0.412

Construction of a new fright terminal along a rural highway has been proposed. During certain periods of the day, significant numbers of large trucks are expected to depart the terminal’s one-lane driveway to access an interstate highway. Developers would like to know if there are an adequate number of time gaps (headways) in the highway traffic to permit about 40 trucks per hour to enter the highway without the need for a traffic signal. To permit a truck to safely enter the highway, a time gap of at least 8 seconds is needed. Assuming that there will be a flow of 850 vehicles on the highway during a design hour, how many gaps or opportunities will there be during the design hour for trucks to enter the highway without a traffic signal? Assume that vehicle arrivals follow a Poisson distribution.

a.849

b.425

c.340

d.212

e.128

Solutions

Expert Solution


Related Solutions

(9) Assume on average 10 passengers arrive per minute. Assuming poisson arrivals and departures, estimate the...
(9) Assume on average 10 passengers arrive per minute. Assuming poisson arrivals and departures, estimate the gain (if any) in ‘average time spent in system per passenger’ if TSA decides to replace 4 type-A security scanners with 3 type-B security scanners. The service rate per scanner for type-A scanners is 3 passengers per minute and type-B scanners is 5 passengers per minute?
Between 4:00PM and 6:00PM the vehicles arrive to the entrance ramp of a regional toll road...
Between 4:00PM and 6:00PM the vehicles arrive to the entrance ramp of a regional toll road at a constant rate of 1740 vehicles per hour. The toll plaza at the entrance ramp has five toll booths, which combined can process up to 34 vehicles per minute. At 4:30PM one of the toll booths is disabled due to electronics malfunction, which reduces the vehicle processing capacity of the toll plaza to 27 vehicles per minute. At 5:00 PM the toll booth...
Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the...
Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places. Part a) What is the probability that exactly two customers arrive in a minute? Part b) Find the probability that more than three customers arrive in a two-minute period. Part c) What is the probability that at least seven customers arrive in three minutes, given...
Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the...
Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places. Part a) What is the probability that exactly two customers arrive in a minute? Part b) Find the probability that more than three customers arrive in a two-minute period. Part c) What is the probability that at least seven customers arrive in three minutes, given...
Airline passengers arrive randomly and independently at the passenger check-in counter. The average arrival rate is 10 passengers per minute.
POISSON PROBABILITY DISTRIBUTION Airline passengers arrive randomly and independently at the passenger check-in counter. The average arrival rate is 10 passengers per minute. to. Calculate the probability that no passenger will arrive within one minute.     μ = 10 in 1 minute x = 0 in 1 minute b. Find the probability that three or fewer passengers will arrive within one minute.     μ = 10 in 1 minute x ≤ 3 in 1 minute >>> P (x = 0) + P...
Customers arrive at a local grocery store at an average rate of 2 per minute. (a)...
Customers arrive at a local grocery store at an average rate of 2 per minute. (a) What is the chance that no customer will arrive at the store during a given two minute period? (b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons? (c)...
A) Phone calls arrive at a particular call center with an average of 12 every minute....
A) Phone calls arrive at a particular call center with an average of 12 every minute. The call center management want the maximum probability of having more calls than staff in any given minute being .2. How many staff are necessary to ensure this? Use Excel to help you find the answer. B) Consider the 1981 Super Bowl commercial from Schlitz involving a live taste test. Schlitz sponsored a live taste test for its beer during the half time of...
Voters arrive at a polling station at an average of 9 per minute (Poisson) where the...
Voters arrive at a polling station at an average of 9 per minute (Poisson) where the service rate is 150 per hour (Poisson). What is the average number of voters in the system with 4 voter booths? (10 pts) What is the minimum number of voting booths needed to keep the average time in the system under 1 minute (must show time)? (10 pts)
1.) Vehicles arrive at an entrance to a recreational park. There is a single gate (at...
1.) Vehicles arrive at an entrance to a recreational park. There is a single gate (at which all vehicles must stop), where a park attendant distributes a free brochure. The park opens at 08:00 am, at which time vehicles begin to arrive at a rate of 480 veh/hr. after 20 minutes the arrival flow rate declines at 120 veh/hr, and it continues at that level for the remainder of the day. If the time required to distribute the brochure is...
The number of people entering a security check-in lineup in a 15-minute interval at a medium...
The number of people entering a security check-in lineup in a 15-minute interval at a medium sized airport can be modeled by the following probability model: ?(?=?)=?−16.6(16.6)??!?=0,1,2,⋯P(X=x)=e−16.6(16.6)xx!x=0,1,2,⋯ Part (a) What does 16.6 represent in the probability model? Select the most appropriate explanation below. A. 16.6 represents how much skewed the distribution of values is. B. 16.6 represents a weighted-average of the number of people who enter the a security check-in lineup every 15-minutes. C. 16.6 is the rate at which...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT