Probability and Statistics

You are missing a key variable here and that is the number of hurricanes in a year. The key thing you need to start all of this is the probability that a given hurricane hits Floriday. All you have is the probability that a hurricane hits Floriday in a given year and that hurricane probability is independent. This means that if you have a year with twice the number of hurricanes, the probability of hits and multiple hits goes up.

So under protest, let's assume that all years have the same number of hurricanes, one. The probability of any given hurricane hitting is 25%. The expected number of hits in ten years is 25% x 10 = 2.5 storms. The expected standard devitiation for a 25% probable event taken 10 at a time is sqrt(p(1-p)N) = sqrt(.25 x .75 x 10) = 1.37 [Note: you could compute this exactly, for such a small data set, but this technique has more general application]. The z score for 2 hurricanes per year is (2 - 2.5) / 1.37 = -.365. Look that up in your handy z-score table and you get 35.8%

For part B, use the same equation in reverse. The z score required for a 99% on the cummulative distribution is 2.33 from your z score table. 2.33 = (x - 2.5) / 1.37 so x = 5.69 hurricanes. Since you can't have fractional hurricanes, call it six.

This technique works a lot better for larger data sets. If you said you have ten storms per year with a hit rate of 2.5% for each storm, you get a standard deviation of sqrt(.025*.975*100) = 1.56. Big change.

hey engineer, thanks for replying to my question. I actually double-checked my post (my question) to make sure that i wrote it right. When you said, "You are missing a key variable here and that is the number of hurricanes in a year," that is the whole problem. What i posted is the whole problem and this is all that i am given for the problem. i was actually thinking that i would need a few more pieces of info in order to start the problem, but what you gave me so far is awesome and a start, i will work with that info. thanks!