Question

• You are responsible for natural disaster recovery planning for the city of Snowbird Beach, North Carolina. Over the past 95 years, your city has been hit by 32 hurricanes, for an annual average of 0.3368 hurricanes per year. What type of distribution describes this situation? What is the probability of getting hit by zero hurricanes in a year? What about at least one? Two or more? Based on your assessment, how many hurricanes should you plan on for budgeting purposes?

Answer 1

Since the time frame is large (95 years) and the probability of occurrence is very low, the type of distribution for the situation should be Poisson distribution. Also, in the give situation

• The outcomes that can be classified as successes or failures (Hurricanes occurred or not)
• The average number of successes (μ) (occurrence Hurricanes) of that occurs in a year is known.
• The probability of occurrence of Hurricanes will occur is proportional to the duration of the time.
• The probability that Hurricanes will occur in an extremely small region (seconds) is virtually zero.

Thus, the situation can be modeled as Poisson distribution.

= annual average of 0.3368 hurricanes per year

Let X be the number of Hurricanes in a year. Then X ~ Poisson( = 0.3368)

Probability of getting hit by zero hurricanes in a year = P(X = 0) = exp(-0.3368) * 0.3368⁰ /0!

= exp(-0.3368) = 0.7140516

Probability of getting hit by at least one hurricanes in a year = P(X 1) = 1 - P(X = 0)

= 1 - exp(-0.3368) = 1 - 0.7140516 = 0.2859484

Probability of getting hit by two or more hurricanes in a year = P(X 2) = 1 - P(X = 0) - P(X = 1)

= 1 - 0.7140516 - exp(-0.3368) * 0.3368¹ /1!

= 1 - 0.7140516 - 0.2404926

= 0.0454558

Since the Probability of getting hit by two or more hurricanes in a year is less than 0.05, we will plan for only one hurricane for budgeting purposes.