8. Final: For recent period of 100 years, there were 530 Atlantic hurricanes. Assume the Poisson distribution is a suitable model, find the probability that less than 3 hurricanes in a randomly selected year. a..1901 O b. None of the above O c.2075 O d. 3701 O e..1016
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- The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005. Use the Poisson distribution to approximate the probability that among 14,000 cars passing through this tunnel, exactly two will have a flat tire. Round your answer to four decimal places. OA. 0.1947 B. 0.1703 OC. 0.1217 OD. 0.8783 OE. 0.146010. The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 6 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period.e. Calculate the probability that there will be a failing student within the first semester.f. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?Suppose that births in a hospital occur randomly at an average rate of 1.9 births per hour. Assume that the probability of a birth is the same for any two time intervals of equal length. a. Which distribution can we use in this case? b. What is the probability that we observe at least 3 births in a 2-hour interval?c. Suppose that births occur randomly in hospital A and hospital B at an average rate of 2.1 births and 3 births per hour, respectively. What is the probability that we observe 7 births in total from the two hospitals in a 1-hour period?
- Despite all efforts by the quality control department, the fabric made at benton corporation always contains a few defects. A certain type of fabric made at this corporation contains an average of 0.51 defects per 500 yards. Using the Poisson formula, find the probability that the number of defects in a given 500-yard piece of this fabric will be between two and four.P(between 2 and 4) =Answer DThe average processing time of a kiosk in a McDonald's store is 4.5 minutes, and there are 3 kiosks. The average interarrival time is 2.5 minutes. Suppose the arrival follows a Poisson process, and the processing time follows an exponential distribution. What is the average time a customer waits for using a kiosk? a. 5.31 minutes b. 2.19 minutes c. 1.47 minutes d. 4.85 minutes
- You and your friends have a large messaging group on GroupMe. The number of messages that are received in the group follows a Poisson distribution with an average of 30 per hour – call this random variable X. Let T be an exponentially distributed random variable that represents the time between messages received. 1. What is the probability that there are between 26 and 35 messages in the next hour? 2. What is the probability that there are exactly 30 messages in the next two hours? 3. What is the average for the variable, T?Time left 1:2 In one sectlon of STAT 1811 course, there are 10 glrls and 20 boys. What Is the probability that in a randomly selected sample of two students from that section both will be glrls? O a. 0.3333 Ob. 0,1034 O c. 0.1111 d. 0.50002. The number of meteors found by a radar system in any 30-second interval under specified a. What is the probability that at least one meteor is found in a one-minute interval? ne meteors appear randomly b. Determine x such that the probability no meteor is found in x-minute interval is 0.02. UTM M UTM UTM c. If there is no meteor appear after two-minute interval, what is the probability that it UTM will appear in the next one and a half-minute interval? m UTM
- Suppose the time it takes for guests to wait for an elevator at the lobby of a certain office building has a uniform distribution between 0 and 4 minutes. What is the probability that, the next time you need to take this elevator, you'll have to wait at most 1.6 minutes? (Your answer should be a decimal. Round to 4 decimal places if necessary.)Please answer this ASAP with complete solutionindicate the units to the final answer if any Draw the necessary graph if any. Round off to four decimal places or in lowest term if your answer is in fraction.