Question

Binomial, Negative Binomial and Hypergeometric Distribution

You are tracking the progression of category 3 hurricanes and are interested in knowing how many of these are upgraded to category 4 hurricanes. Past data indicates that category 3 hurricanes have a probability of 0.01 of being upgraded to a category 4 hurricane. Assume that these probabilities continue to represent future hurricane behavior. Assume that, due to advances in hurricane forecasting technology, meteorologists know that there will be 538 category 3 hurricanes during this year’s hurricane season. You want to use this information to predict the behavior of these hurricanes during this year’s hurricane season. Use this information to answer questions 1 to 5.

1. What is the expected number of category 3 hurricanes upgraded to category 4 hurricanes based on the data, assuming meteorologists’ predictions of the number of category 3 hurricanes are correct (round to 2 digits)?

2. What is the probability that there are exactly three category 3 hurricanes that will be upgraded to category 4 hurricanes this hurricane season? (use 3 decimal places)

3. What is the probability that more than two category 3 hurricanes will be upgraded to category 4 hurricanes this hurricane season? (Use 3 decimal places)

4. Fast forward into the future as the year’s hurricane season unfolds and category 3 hurricanes occur one at a time. What is the probability that the first hurricane that is upgraded to a category 4 hurricane is the 28^th category 3 hurricane of the season? (use 4 decimal places)

5. How many category 3 hurricanes would you expect to occur before one is upgraded to a category 4 hurricane for the first time?

Answer 1

1,2,3 will be solved using binomial distribution and 4,5 using negative binomial.