Probability of Finding Shrubs in Jojoba Acres

In summary, an agronomist has found an average of 2 shrubs per acre of jojoba, following a Poisson distribution. To find the probability of finding 5 plants, we first need to determine the area of land (1, 2, or 3 acres) that the agronomist should search. Using the Poisson distribution, we can calculate the probability for each scenario. Additionally, for part (b), there may be some restrictions on the probability due to the word "next". Further clarification is needed to accurately calculate the probability for this scenario.
  • #1
Cyrus
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4)An agronomist has found an average of 2 shrubs per acre of jojoba, which serves as the source for transmission oil. Find the Following probabilities:
a) That 5 plants will be found when the number of acre search is (1) one; (2) two;
or (3) three.
b) That no plants will be found in searching the next (1) .5 acre; (2) 1 acre; or (3)
1.5 acres

I want to just do this, but I don't think I can:

The Agronomist finds an average of 2 shrubs per 1 acre jojoba. μ = 2

The probability is given by: μ = np, hence: p = (μ/n)

a.) (1) p = (2/5) = 0.4 (2) p = (2)/(5/2) = 0.8 (3) p = 1.2


120% does not seem rational. If its going to happen, it should be 100% at most.
 
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  • #2
Hi!

First things first,definitions! Let X be the random variable for the number of shrubs per acre of jojoba.

In my opinion, X should follow a Poisson distribution, as there is theoretically no limit to the number of shrubs we can find, instead of a Binomial model as seen in your calculations. Hence, [tex] X \sim P_0(2) [/tex]
With this, you should be able to proceed with your working for (a).

As for part (b), I think we should pay some attention to the word "next". This probably means that there is some restriction on the probability. I think the question means that the agronomist should find 5 plants in the first area of land... but which area (1, 2, or 3 acres) should we use?
 

1. What is the probability of finding shrubs in Jojoba Acres?

The probability of finding shrubs in Jojoba Acres depends on various factors such as soil type, climate, and region. It is not possible to determine the exact probability without conducting a thorough study of the area.

2. How is the probability of finding shrubs in Jojoba Acres calculated?

The probability of finding shrubs in Jojoba Acres can be calculated by dividing the number of shrubs found in the area by the total number of plants in the area. This will give a rough estimate of the probability, but it may not be accurate due to various factors that can affect the growth of shrubs.

3. Are there any specific types of shrubs that are more likely to be found in Jojoba Acres?

Yes, there are specific types of shrubs that are more likely to be found in Jojoba Acres depending on the climate and soil conditions. For example, desert shrubs like creosote bush and white sage are commonly found in this area.

4. How does the probability of finding shrubs in Jojoba Acres impact the local ecosystem?

The probability of finding shrubs in Jojoba Acres plays a crucial role in the local ecosystem. Shrubs provide important habitat and food sources for animals, help prevent soil erosion, and contribute to the overall biodiversity of the area.

5. Is there a way to increase the probability of finding shrubs in Jojoba Acres?

There are various ways to increase the probability of finding shrubs in Jojoba Acres, such as planting shrubs in the area, providing proper care and maintenance, and creating favorable conditions for shrub growth. However, it is important to consider the natural conditions of the area and choose native shrub species that are well-suited for the environment.

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