An engineer counts 400 veh/hr at a specific highway location. Assuming that the vehicles arrive based on a poisson distribution, estimate the probabilities of having 0, 1, 2, 3, 4, and 5 or more vehicles arriving over a 20-second interval.
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An engineer counts 400 veh/hr at a specific highway location. Assuming that the vehicles
arrive based on a poisson distribution, estimate the
more vehicles arriving over a 20-second interval.
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- Consider an auto insurance portfolio where the number of accidents follows a Poisson distribution with parameter lamda = 1000. Suppose the damage sizes for separate accidents are i.i.d. (independent identically distributed) r.v.'s having an exponential distribution with a mean of $2500. Each policy involves a deductible of $500. Let N1 be the number of accidents that result in claims, and N2 be the number of accidents that do not result in claims. Answer the following questions 1-5. 1. Are N1, N2 dependent? 2. What is the name of the distributions of N1, N2? Compound Poisson or Marked Poisson? 3. What is the mean and variance of N1? 4. What is the mean and variance of N2? 5. Which of the number is close to the probability that N1 will not be larger than 790? (Hint: to what distribution is the Poisson distribution with a parameter of lamda close for "large" lamda's?An engineer has built a simulation model of a small factory, run an experiment with the model using 15 replicates, and determined at 90% confidence that the mean time an entity spends in the system is in the range of 24 min to 28 min. The data are normally distributed. Based on this information, what can the engineer say about entity time-in-system?A -The population mean time-in-system must be in the interval 24 min to 28 min. B- The largest mean time-in-system for any one of the 15 replicates was 28 min. C- If the engineer were to run a 16th replicate, the mean time-in-system would be in the interval 24 min to 28 min. D. The probability that the population mean time-in-system is greater than 28 min can be estimated as 5%.The number of earthquakes per day in the world has a Poisson distribution with parameter ?= 55. Suppose that the random variable X is the number of earthquakes occurring in one day in the world. Let the random variable Y be the total number earthquakes occurring in the world in 3 days. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.a. For our model, what is expected value of X? b. What is the probability that X = 55? c. What is the probability that X > 55? d. What is the probability that X >60? e. What is the smallest value C so that there is at least a 0.9 probability of no more than C earthquakes in a day? f. Y also has a Poisson distribution. What is the parameter ?y for Y? g. What is the standard deviation of X? h. What is the probability Y =164? i. What is the probability that Y < 164? j. What is the probability that X>60 given that X>55?
- On average, Nancy has noticed that 23 trucks pass by her apartment daily (24 hours). In order to find the probability that more than 5 trucks will pass her apartment in a 6-hour time period using the Poisson distribution, find the average number of trucks per 6 hours. Round your answer to three decimal places, if necessary.The downtime per day for a certain computing facility has averaged 4.0 hours and a standard deviation of 1.98 for the last year. Find the probability that the average daily downtime for a period of 20 days is between 1 and 5 hours.A car hire firm has two cars, which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson distribution with mean 1.5. Calculate the proportion of days on which neither car is used and the proportion of days on which some demand is refused. (e-5 = 0.2231).
- The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3.500 accidents per year. 1. Find the mean waiting time between accidents. (Round the final answer to four decimal places.) 2. Find the standard deviation of the waiting times between accidents. (Round the final answer to one decimal place.) 3. Find the probability that more than one year elapses between accidents. (Round the final answer to four decimal places.) 4. Find the probability that less than one month elapses between accidents. (Round the final answer to four decimal places.) 5. If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year? (Round the final answer to four decimal places.)A hot dog concession at Safeco Field sells an average of 54.67 hot dogs per hour (believed to follow a Poisson Distribution). How many hot dogs should the vendor stock in order to be 93% sure it has enough hot dogs for 1.5 hour(s)? F−1(0.93)=The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
- Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. a)What is the average number of cars in the garage (not including the parking lot)? b) How long (in minutes) do vehicles wait on average in the adjacent parking lot? c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the…On average, Nancy has noticed that 15 trucks pass by her apartment daily (24 hours). In order to find the probability that more than 3 trucks will pass her apartment in a 5-hour time period using the Poisson distribution, find the average number of trucks per 5 hours. Round your answer to three decimal places, if necessary.On average, Nancy has noticed that 27 trucks pass by her apartment daily (24 hours). In order to find the probability that more than 2 trucks will pass her apartment in a 4-hour time period using the Poisson distribution, find the average number of trucks per 4 hours. Round your answer to three decimal places, if necessary.
