In one town, the number of burglaries in a week has a Poisson distribution with a mean of 1.9 burglaries. Find the probability that in a randomly selected week the number of burglaries is at least three. Use the Poisson
Distribution to find the indicated probability.
A) 0.8290
B) 0.1710
C) 0.1253
D) 0.2963
E) 0.7037

Question

Quizplus · Accepted Answer

We can use the Poisson distribution formula to solve this problem:
P(X ≥ 3) = 1 - P(X < 3)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
P(X = k) = (e^(-λ) * λ^k) / k!
where λ = 1.9 (mean)
P(X = 0) = (e^-1.9) * 1.9^0 / 0! = 0.1499
P(X = 1) = (e^-1.9) * 1.9^1 / 1! = 0.2849
P(X = 2) = (e^-1.9) * 1.9^2 / 2! = 0.2709
P(X < 3) = 0.1499 + 0.2849 + 0.2709 = 0.7057
P(X ≥ 3) = 1 - 0.7057 = 0.2943 ≈ 0.2963 (rounded to four decimal places)
Therefore, the answer is D.

In One Town, the Number of Burglaries in a Week