Use the Poisson Distribution to find the indicated probability.
-On one tropical island, hurricanes occur with a mean of 2.74 per year. Assuming that the number of hurricanes can be modeled by a Poisson distribution, find the probability that during the next 3 years the number of
Hurricanes will be 2.
A) 0.0249
B) 0.0091
C) 0.2424
D) 0.0010
E) 0.0646

Question

Quizplus · Accepted Answer

The Poisson distribution formula is:

P(X = k) = (e^-λ * λ^k) / k!

where X is the random variable (in this case, the number of hurricanes per year), k is the specific value we want to find the probability for (in this case, 2 hurricanes in 3 years), e is the mathematical constant approximately equal to 2.71828, and λ is the mean (average) number of hurricanes per year (2.74 in this case).

To find the probability that there will be exactly 2 hurricanes in 3 years, we need to use the Poisson distribution formula with λ = 2.74 * 3 = 8.22 (since we are looking at 3 years instead of 1 year).

P(X = 2) = (e^-8.22 * 8.22^2) / 2!

P(X = 2) = 0.0091

Therefore, the probability that there will be exactly 2 hurricanes in 3 years is 0.0091 or approximately 0.91%.

The best choice is B.

Use the Poisson Distribution to Find the Indicated Probability