Question

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 9.5.
Find the probability of no dandelions in an area of 1 m².
P(X = 0) =

Answer 1

The probability of no dandelions in an area of 1 m² is approximately 0.0001125352.

Step-by-step explanation:

To find the probability of no dandelions in an area of 1 m², we need to use the Poisson distribution.

The mean number of dandelions per square meter is given as 9.5.

The Poisson distribution formula is P(X = k) = (e^-λ * λ^k) / k!, where λ is the mean and k is the number of events.

In this case, λ = 9.5 and we want to find P(X = 0), so k = 0.

Plugging these values into the formula, we get :

P(X = 0) = (e^-9.5 * 9.5^0) / 0!

= e^-9.5.

Using a scientific calculator, we can calculate e^-9.5 to be approximately 1.125352e-04, or 0.0001125352.