Final answer:
To determine the probability of there being no dandelions in a 1 m² area, the Poisson distribution is the most suitable choice, given that it pertains to predicting the occurrence of events in a fixed space interval and under a known average rate. The correct answer is option a.
Step-by-step explanation:
To find the probability of no dandelions in an area of 1 m², we should choose the Poisson distribution. This is because the Poisson distribution is ideally suited for situations where we want to determine the probability of a certain number of events occurring in a fixed interval of space or time, given a known average rate of occurrence and that the events happen independently of each other.
The key factors for using the Poisson distribution are:
- The events are occurring independently.
- The average rate of occurrence is known.
- We are dealing with a fixed interval of space or time.
Given that these conditions are met for the case of no dandelions over a square meter, option a. Poisson distribution would be the correct choice. In contrast, the other options like the binomial, normal, and hypergeometric distributions are not as well-suited for this particular scenario, as:
- The binomial distribution is used when there is a fixed number of trials with only two possible outcomes (success or failure) per trial.
- The normal distribution typically approximates a binomial distribution when the number of trials is large, and the probability of success is neither very small nor very large.
- The hypergeometric distribution is related to sampling without replacement from a finite population, which doesn't fit the occurrence of dandelions in a continuous space.
Hence, the correct answer to the student's question is option a. Poisson distribution.