Question

4. In a study of the effect of an insecticide against gypsy moths, a large area of land was sprayed. Later the area was examined for live adult insects by randomly selecting and surveying 10 m x 10 m. Past experience has shown the average number of a live adult insects per square after spraying to be 5. If these insects are Poissonally distributed, find: (a) the probability that a square will contain exactly 5 live adult insect. (b) the probability that a square will have more than 5 live adult insects.

Answer 1

4. Solution :

Given that average λ = 5

=> Formula : for poisson distribution , P(x,λ) = e^(-λ)*λ^x/x!

(a)
=> P(x = 5) = e^(-5)*5^5/5!

= 0.1755

(b)
=> P(x > 5) = 1 - P(x <= 5)

= 1 - [P(x = 5) + P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1) + P(x = 0)]

= 1 - [e^(-5)*5^5/5! + e^(-5)*5^4/4! + e^(-5)*5^3/3! + e^(-5)*5^2/2! + e^(-5)*5^1/1! + e^(-5)*5^0/0!]

= 1 - [0.1755 + 0.1755 + 0.1404 + 0.0842 + 0.0337 + 0.0067]

= 0.3840