Example 4.7 A piece of radioactive material emits alpha-particles accordingto a Poisson process with an intensity of 0.84 particle per second. A counterdetects each emitted particle, independently, with probability 0.95. In a 10-second period the number of detected particles is 12. What is the probabilitythat more than 15 particles were emitted in that period?

Answered: Image /qna-images/answer/b17d16c9-3f47-430c-8bd2-3b52053b4e75.jpg

Answered: Example 4.7 A piece of radioactive…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?
4.3 Section Exercise 30 Question 3 of 8 (1 point) View problem in a pop-up The Gift Basket Store has the following premade gift baskets containing the following combinations in stock. Сandy Mugs Cookies 17 16 15 Coffee 14 14 17 Tea Download data Choose 1 basket at random. Find the probability that it contains the following combinations. Enter your answers as fractions or as decimals rounded to 3 decimal places. Part 1 out of 3 Tea or mugs P (tea or mugs)= NEXT CHECK
12. A laser printer on a local area computer network is capable of printing eight pages per minute. Print requests arrive randomly and independently at an average rate of 20 per hour and are placed in a queue according to their arrival times. The average request results in ten printed pages. Suppose that the time it takes to process each request is exponentially distributed and that the print times for different jobs are independent. a. What is the probability that this printer will be idle for the next 5 minutes if the queue is currently empty? b. What is the probability that the next request will take more than 2 minutes to process? c. There is currently one job in the queue and it has been active for the last 5 minutes. What is the probability that this job will still be active I minute from now? d. There are currently five jobs in the queue-one active and four waiting to be processed. You submit a job to this printer and it becomes the sixth job in the queue. What is the…
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A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. What is the arrival rate? (Include the units.) What is the service rate? (Include the units.) Find the probability that the employee is idle.
What is the probability of getting at least one tail if two unbiased coins are independently tossed? а. 1/4 b. 1/2 с. 7/8 d. 3/4
Question 20. A town has a clinic where people go to donate blood. One third of the persons donating blood at each of these clinics have O+ blood. What is the probability that in a randomly chosen day, it takes six donors to find two O* donor in the 6th donor of the day? (a) 0.3292 (b) 0.0329 (c) 0.1097 (d) 0.1314
1. Power companies severely trim trees growing near their lines to avoid power failures due to falling limbs in storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but the chemical kills some of the trees. Suppose that one such chemical would kill 20% of sycamore trees. The power company tests the chemical on 250 sycamores. Consider this a SRS from the population of all sycamore trees. Calculate the probability that less than 24% of the tress in the sample are killed. (Hint: Shape, Center, Spread, Curve, Calculations, Conclusion....)
A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 11 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 22 insects will die? Round your answer to four decimal places.
Question 7 A small regional carrier accepted 14 reservations for a particular flight with 12 seats. 6 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 48% chance, independently of each other. (Report answers accurate to 4 decimal places.) Find the probability that overbooking occurs. Find the probability that the flight has empty seats. Question Help: DVideo DPost to forum Submit Question
A new surgery is successful 85% of the time. If the results of 10 such surgeries are randomly sampled, what is the probability that fewer than 9 of them are successful? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.) ?
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