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- The number of vehicles arriving at a toll booth, per minute, were observed as follows: 0, 3, 1, 2, 0, 1, 1, 1, 2, 0, 1, 4, 3, 1, 1, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0 (1) Assuming that the arrival rate of vehicles at the toll booth is a Poisson process, estimate the mean arrival rate using the method of moments. (2) Perform a chi-square test to determine the validity of the Poisson distribution at the 1% significance level.Suppose the log-ins to a company's computer network follow a Poisson process with an average of three counts per minute. What is the mean time between counts? What is the standard deviation of the time between counts?Q 4: Mr. Ahmed who is a manager at PVR Multiplex Muscat has conducted a survey to investigate the number of people visited the theatre in the last 30 days. The number of people visited the theatre in the last 30 days are: 30, 36, 39, 37, 36, 54, 38, 33, 37, 33, 33, 36, 32, 48, 42, 38, 36, 35, 30, 33, 39, 37, 33, 36, 30, 39, 44, 32, 44 and 50. Find out the grouped frequency distribution using 5 classes. Which graph will be suitable to present the grouped frequency distribution? Give reasons to your answer Cumulative frequency and relative frequency are same. Discuss critically
- The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.62. Part a) What is the probability that the time between consecutive customers is less than 15 seconds? Part b) Find the probability that the time between consecutive customers is between ten and fifteen seconds. Part c) Given that the time between consecutive customers arriving is greater than ten seconds, what is the chance that it is greater than fifteen seconds?The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.75. Part a) What is the probability that the time between consecutive customers is less than 15 seconds? Part b) Find the probability that the time between consecutive customers is between ten and fifteen seconds. Part c) Given that the time between consecutive customers arriving is greater than ten seconds, what is the chance that it is greater than fifteen seconds?please show steps neatly with answer.
- Suppose population 1 consists of all students who picked up all the tests they completed prior to taking the final exam. Suppose population 2 consists of all students who had one or more tests that they completed that were not picked up prior to taking the final exam. Based on years of grading final exams and observing grades, STAT 210 instructors conjecture that the mean final exam grade for all students who picked up all their tests is greater than the mean final exam grade for all students who had one or more tests that were not picked up. A simple random sample of 56 students who picked up all tests they completed was selected, and the mean score on final exam for this sample of students was 83 with a standard deviation of 10.4. An independent simple random sample of 51 students who had one or more tests that were not picked up was selected, and the mean score on the final exam for this sample of students was 67 with a standard deviation of 24.2. Both distributions are skewed…The time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with 2-0.0004. Assuming we have a large number of computers. a) What is the expected life of a fan (in hours)? b) What is the mean time until the tenth fan failure? c) What is the expected number of fans failing in the next 5000 day.Fish swim past a sensor in the river following a poisson process. On average, 1 fish passes by every 2.693 minutes. The number of fish that pass by in 1 hour is distributed as Poisson(ƛ). What is ƛ?
- The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.47. Part a) What is the probability that the time between consecutive customers is less than 15 seconds? Part b) Find the probability that the time between consecutive customers is between ten and fifteen seconds. Part c) Given that the time between consecutive customers arriving is greater than ten seconds, what is the chance that it is greater than fifteen seconds?Please helpThe Johnson & Johnson Company operates 6 identical machines that are serviced by a single technician when they breakdown. These breakdowns occur according to the Poisson distribution and average 0.03 breakdowns per machine operating hour. Average repair time for a machine is 5 hours and follows the exponential distribution. a) What percent of the technician's time is spent repairing machines? Answer in 4 decimal places. Blank 1 b) On average, how long is a machine out of service because of a breakdown? Answer in 2 decimal places. Blank 2 c) On average, how many machines are out of service? Answer in 1 decimal place. Blank 3 Blank 1 Blank 2 Blank 3 Add your answer Add your answer Add your answer