1)
Let X denote the number of buses that arrive in a 5-minute interval. Then
a)
Required probability =
b)
We know that if , then
So,
Suppose that busses arrive at a station with constant rate per minute. Conferences 1. Assume that...
Customers arrive at a gas station with the rate λ = 4 per hour. The station operates for 12 hours, from 7 AM 7 PM 1. Find the probability of having at least one customer from noon to 3 PM 2. Find the conditional probability that after 2 hours since the station was open, there will be at least three customers, given that exactly one customer arrived by the end of the first hour
During lunchtime at a certain fast food restaurant, customers arrive at an average rate of 7 customers every 5 minutes. assume a poisson distribution to find the probability that: A) exactly 12 customers arrive in a given 10 minute interval (perform this calculation using an appropriate formula, showing the setup.) b) between 5 and 10 customers (inclusive) arrive in a given 5 minute interval (show how you can answer this from the table) c) after a customer arrives, find the...
Trucks arrive at a loading/unloading station according to a Poisson process with a rate of 2 trucks per hour. Determine the probability that at least 3 trucks will arrive at the station in the next 30 minutes, A. 0.86 B. 0.59 C. 0.13 D. 0.81 E. 0.08
Customers arrive at a local ATM at an average rate of 15 per hour. Assume the time between arrivals follows the exponential probability distribution. Determine the probability that the next customer will arrive in the following time frames. a) What is the probability that the next customer will arrive within the next 5 minutes? b) What is the probability that the next customer will arrive in more than 8 minutes? c) What is the probability that the next customer will...
4. Suppose that spectators arrive to a baseball game according to a Poisson process with a rate of 10 per minute. If a spectator wears a baseball jersey with probability 1, what is the probability that no spectator wearing a baseball jersey will arrive during the first four minutes? 4. Suppose that spectators arrive to a baseball game according to a Poisson process with a rate of 10 per minute. If a spectator wears a baseball jersey with probability 1,...
Cars arrive at a car wash at the rate of 18 cars per hour. Assume that cars arrive independently and the probability of an arrival is the same for any two time intervals of equal length. (2 pts.) Compute the probability of at least three arrivals in a 5-minute period. (2 pts.) Compute the probability of at most two arrivals in a 10-minute period.
Customers arrive at a garage at an average rate of 2 per five minute period. What is the probability that less than 15 arrive in a one hour period?
The times between parts arrive a manufacturing station is exponentially distributed with mean of 0.5 minute. What is the value of parameter? What is the median time between the parts arrive? What is the standard deviation? What is the 80th percentile? Find the probability of that more than 1 minute elapse between part arrivals. After manufacturing, computer disks are tested for errors. Let X be the number of errors detected on a randomly chosen disk. The following table presents the...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute a. Compute the probability of no arrivals in a one-minute period (to 6 decimals) b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals) c. Compute the probability of no arrivals in a 15-second period (to 4 decimals) d. Compute the probability of at least one arrival in a 15-second period (to 4...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 8 passengers per minute. a. Compute the probability of no arrivals in a one-minute period (to 6 decimals). b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). c. Compute the probability of no arrivals in a 15-second period to 4 decimals). d. Compute the probability of at least one arrival in a 15-second period (to 4...