Question

Suppose on the average 2 hurricanes form in the Atlantic Ocean per season. What is the probability that at least 5 Atlantic hurricanes occur during next season. Write all probability values as numbers between 0 and 1. Use at least two decimals.

Answer 1

Solution :

Given that ,

mean = = 2

Using Poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

P(X 5) = 1 - P(X < 5)

= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) -P(X = 4)

= 1 - (e^-2 * 2⁰⁾ / 0! - (e^-2 * 2¹⁾ / 1! - (e^-2 * 2²⁾ / 2! - (e^-2 * 2³⁾ / 3! - (e^-2 * 2⁴⁾ / 4!

= 0.05265

Probability = 0.053