Dandelions are studied for their effects on crop production

Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per 10 square foot was found to be 7. Find the probability of at least one dandelion in an area of 1 square foot. You have to define an appropriate random variable, state its distribution and the associated parameter value(s), and express the event of interest in terms of the random variable.

Solution

2.

The random variable x is the amount of dandelions per 1 sq ft.

Its distirbution is Poisson, with mean (7 dandelions/10 sq ft)*(1 sq ft) = 0.7 dandelions/sq ft.

          
Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    0.7      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.496585304
          

Therefore,

P(at least 1) = 1 - P(0) = 0.503414696 [ANSWER]