Determine the following probabilities for a 50 year flood by using a Poisson's distribution: a. What is the probability that exactly one 50 year flood in next 5- years? b. What is the probability that two or more 50 years floods in a 10- year interval? c. What is the probability of having no 50 years flood next year?
Added by Gonzalo H.
Step 1
Step 1: Assume flood events follow a Poisson process with rate λ = 1/50 per year (since on average one 50-year flood every 50 years). Show more…
Show all steps
Close
Your feedback will help us improve your experience
Aarti Kumari and 100 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
In a particular state, a major flood happens once every 3 years on average. If you can assume floods are independent, and that two floods cannot happen simultaneously, find the following: a) The probability that a flood happens within the first 5 years. b) The probability that a flood happens after the first 2 years. c) If there has been no flood for 4 years, what is the probability there is a flood within the next 2 years? d) The expected time until a flood happens, and the standard deviation. e) Find the 50th percentile of the time until a flood.
Aarti K.
Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.2 per year. a. Find the probability that, in a year, there will be 3 hurricanes. b. In a 45-year period, how many years are expected to have 3 hurricanes? c. How does the result from part (b) compare to a recent period of 45 years in which 5 years had 3 hurricanes? Does the Poisson distribution work well here?
Madhur L.
A country is subject to natural hazards such as floods, earthquakes, and tornadoes. Suppose earthquakes occur according to a Poisson process with a mean rate of 10 per year; tornado occurrences are also Poisson-distributed with a mean rate of 0.3 per year. There can be either one or no flood each year; hence the occurrence of a flood each year follows a Bernoulli sequence, and the mean return period of floods is 5 years. Assume floods, earthquakes, and tornadoes can occur independently. If no hazards occur during a given year, it is referred to as a "good" year. What is the probability that at least 2 of the next 5 years will be good years? What is the probability of only one incidence of a natural hazard in a given year? [20 points] A town is bordered by two rivers as shown in the following figure. Levees A and B were constructed to protect the town from high water in the rivers. The levees were both designed for floods with return periods of 5 and 10 years, respectively. Assume that the events of flooding from the two rivers are statistically independent. Determine the probability that the town will encounter flooding in a given year.
Lucas F.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD