Final answer:
The question asks for calculations based on the Poisson distribution, related to the number of traffic accidents in a given time frame. To answer, one must apply the Poisson distribution formulas to calculate probabilities for various scenarios involving the frequency of accidents.
Step-by-step explanation:
The question pertains to the application of the Poisson distribution to model the frequency of events, such as traffic accidents, within a given period. When the average number of occurrences is known (e.g., three accidents per week), one can calculate various probabilities related to these events. Specifically:
- Probability of at most two accidents per week can be found using the cumulative distribution function of the Poisson distribution.
- Probability of at least two weeks between accidents involves the interpretation of the distributions' properties and possibly its relation to the exponential distribution.
For the given traffic accidents example with an average of three per week, to calculate the probability of at most two accidents, we use the formula for the Poisson probability mass function and sum the probabilities of 0, 1, and 2 accidents.
To address the question about the probability of at least two weeks between accidents, one could use the exponential distribution, which describes the time between Poisson events.