Discrete distributions A GIS firm is investigating the safety of a dangerous road stretch in the Himalayas. Historical data  indicates an average of 6 landslides per year over this stretch. The number of landslides is distributed  according to a Poisson distribution. The firm wants to calculate the probability of exactly 3 landslides  in any year

someone finds that an average of 1.6 cars approach the intersection every minute. assuming the number of cars that approach this intersection follows a Poisson distribution, what is the probability that 3 or more cars will approach the intersection within a minute?

Data documented for weather events in the state of Montana is obtained over a period of years and includes hail storms causing property damage. The data is analyzed and appears to fit a poison distribution with an average of 3.3 damaging hail storms per year.  What is the likelihood that between 2 and 4 damaging hail storms are seen in a randomly selected year?  please show using Poisson.dist function  What is the probability that at least one significant hail storm causing damage is experienced in the coming year?  What is the likelihood that Montana would experience between 5 and 7 damaging hailstorms over a two year period?  What is the likelihood that Montana would experience more than 7 damaging hail storms over a two-year period? please show all steps using excel formulas

In a recent year, a hospital had 4463 births. Find the mean number of births per day, then use that result and the Poisson distribution to find the probability that in a day there are 14 births. Does it appear likely that on any given day, there will be exactly 14 births?

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In a recent​ year, a hospital had 4142 births. Find the mean number of births per​ day, then use that result and the Poisson distribution to find the probability that in a​ day, there are 13 births. Does it appear likely that on any given​ day, there will be exactly 13 ​births?

The duration of a professors class has a continuous uniform distribution between 50.0 minutes and 52.0 minutes. If one class is randomly selected, find the probability that the professors duration of the class is more than 50.9 minutes.

poisson distribution

A certain kind of sheet metal has, on average, 4 defects per 20 square feet.Assuming a Poisson distribution, find the probability that a 28 square foot metal sheet has at least 7 defects. Round your answer to three decimal places.