Hurricane Isabel struck the North Carolina Coast, causing extensive damage. For

Question

Hurricane Isabel struck the North Carolina Coast, causing extensive damage. For several days prior to reaching land the National Hurricane Center had been predicting the hurricane would come on shore between Cape Fear, North Carolina, and the North Carolina-Virginia border. It was estimated that the probability the hurricane would actually strike in this area was 0.90. In fact, the hurricane did come on shore almost exactly as forecast and was almost in the center of the strike area. The National Hurricane Center forecasts that the hurricane will hit the strike area with a probability of 0.90. a. What probability distribution does this follow? (Click to select) b. If there are 13 hurricanes this season, what is the probability that all reach the strike area? (Round your answer to 4 decimal places.) Probability c. What is the probability at least one of 13 hurricanes reaches land outside the strike area? (Round your answer to 4 decimal places.) Probability

Explanation / Answer

a. The distribution followed here is the Binomial distribution because all or some of the hurricanes may strike with probability p=0.9 or miss the strike area with probability 0.1

b. If all 13 hurricanes reach the strike area, requited probability = 13C13 * 0.9^13 = 0.254

c. The probability for at least one hurricane reaching outside the strike area = 1- Probability that all 13 hurricanes strike in the strike area = 1-0.254 = 0.746

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