Question

A certain area of the eastern United States is affected, on average, by 6 hurricanes a year. Calculate the probability that this area will be affected by at least 7 hurricanes for a certain year.

Answer with up to 4 decimals.

Answer 1

X ~ Poi ( )

Where = 6

Poisson probability distribution is

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

P(X >= 7) = 1 - P(X <= 6)

= 1 - [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) ]

= 1 - [ e^-6 + e^-6 * 6 +e^-6 * 6² / 2! +e^-6 * 6³ / 3! +e^-6 * 6⁴ / 4! +e^-6 * 6⁵ / 5! +e^-6 * 6⁶ / 6! ]

= 0.6993