SOLUTION: Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per square meter was found to be 9.9. Find the probabil

Question 1209744: Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per square meter was found to be 9.9.
Find the probability of no dandelions in an area of 1 m².

Find the probability of at least one dandelion in an area of 1 m².
P(at least one) =
0.99995
Correct
Find the probability of at most two dandelions in an area of 1 m².

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
You're on the right track using the Poisson distribution! Here's how to calculate the probabilities:
**1. Probability of no dandelions:**
* The Poisson distribution formula is: P(x) = (e^-μ * μ^x) / x!
* Where:
* P(x) is the probability of x events occurring
* e is the base of the natural logarithm (~2.71828)
* μ is the mean number of events (9.9 dandelions per square meter)
* x is the number of events we're interested in (0 dandelions)
* x! is the factorial of x (0! = 1)
* Plugging in the values: P(0) = (e^-9.9 * 9.9^0) / 1
* Calculating this gives you approximately 0.0000504
**2. Probability of at least one dandelion:**
* This is the complement of having no dandelions. So:
* P(at least one) = 1 - P(0)
* P(at least one) = 1 - 0.0000504
* P(at least one) ≈ 0.9999496 (which rounds to 0.99995 as you correctly stated)
**3. Probability of at most two dandelions:**
* This means we want the probability of having 0, 1, or 2 dandelions. We need to calculate each of these probabilities and add them together:
* P(0) = 0.0000504 (calculated above)
* P(1) = (e^-9.9 * 9.9^1) / 1! ≈ 0.0004988
* P(2) = (e^-9.9 * 9.9^2) / 2! ≈ 0.002469
* P(at most two) = P(0) + P(1) + P(2)
* P(at most two) ≈ 0.0000504 + 0.0004988 + 0.002469
* P(at most two) ≈ 0.0030182
**Therefore, the probability of at most two dandelions in an area of 1 m² is approximately 0.0030182**

RELATED QUESTIONS
Dandelions are studied for their effects on crop production and lawn growth. In one... (answered by aisha_amiri@ymail.com)

A farmer is going to divide her 50 acre farm between two crops. Seed for crop A costs $50 (answered by Solver92311)

A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the... (answered by LinnW)

A researcher is interested in finding a 95% confidence interval for the mean number... (answered by Boreal)

A researcher is interested in finding a 90% confidence interval for the mean number... (answered by ewatrrr)

What price do farmers get for the peach crops? in the third week of June, a random sample (answered by stanbon)

A manufacturer is studying the effects of cooking temperature, cooking time, and type of... (answered by stanbon)

A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $20 (answered by ikleyn)

A farmer is going to divide her 40 acre farm between two crops. Seed for crop A costs $10 (answered by stanbon,Alan3354)