Suppose that patients to a dentist's office arrive according to a Poisson process with rate of 5 p hour. What is the expected time (in hours) until the 8th patient arrive at the dentist's office?
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- Suppose we know that the number visits to a webpage can be modeled as a Poisson Process with rate α = 4 per minute. The probability that the webpage gets exactly 10 visits during a particular 2 minute period is approximatelyStarting at time 0, amusement park attendees enter the park and arrive according to a Poisson process with rate equal to 48 per hour. If 10 attendees arrive in the first minute, what is the expected number of attendees that arrive in the first two minutes?Assume that arrivals of cars at a gas station can be modeled by a Poisson process with rate 2 cars per hour. What is the probability that one has to wait at least 3 hours for the arrival of 3 cars?
- Suppose the average number of customers going through a drive-thru in a one hour period is 30 and follows a Poisson process. What is the probability that the person working the drive-thru window has to wait more than 32 minutes for 8 customers come through?Suppose that telephone calls arriving at a particular switchboard follow a Poisson process with an average of 5 calls coming per minute. What is the probability that up to a minute will elapse by the time 2 calls have come in to the switchboard? 2 decimal places~if calls to your cell phone are a Poisson process with a constant rate lambda=2 calls per hour, what's the probability that, if you forget to turn your phone off in a 1.5 hour movie, your phone rings during that time? ~How many phone calls do you expect to get during the movie?
- The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of five per hour. What is the probability that exactly four arrivals occur during a particular “half an hour”?Suppose that on average, 5 customers arrive at a shop during a 1-hour period. Assume arrival times of customers follow a Poisson Process. Find the probability that no customer will arrive within 5 minutes. (in percent)Suppose taxicab arrivals from 3 to 5 p.m. are a Poisson process. If the cabs arrive at an average rate of 18 per hour, what is the probability that a person will have to wait up to 5 minutes for a cab?
- The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. What is the probability that there are more than two calls in a 20 minutes interval?Suppose that earthquakes occur according to a Poisson process with rate λ = 0.2 per day. (a) What is the probability that there will be 2 or fewer earthquakes in April? (b) Starting from now, what is the probability that the second earthquake will occur within a week?Assume that the number of phone calls that reach a specific phone center follow the Poisson rate at a rate of 5 calls per second Calculate the probability of 7 calls arriving in a second and a half?