The following data show the number of hurricanes to directly strike the mainland U.S. each decade. A major hurricane is one with a strength rating of 3, 4 or 5. Decade Total Number of Hurricanes Number of Major Hurricanes 1941 – 1950 24 10 1951 – 1960 17 8 1961 – 1970 14 6 1971 – 1980 12 4 1981 – 1990 15 5 1991 – 2000 14 5 2001 – 2004 9 3
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The following data show the number of hurricanes to directly strike the mainland U.S. each decade. A major hurricane is one with a strength rating of 3, 4 or 5.
| Decade | Total Number of Hurricanes | Number of Major Hurricanes |
|---|---|---|
| 1941 – 1950 | 24 | 10 |
| 1951 – 1960 | 17 | 8 |
| 1961 – 1970 | 14 | 6 |
| 1971 – 1980 | 12 | 4 |
| 1981 – 1990 | 15 | 5 |
| 1991 – 2000 | 14 | 5 |
| 2001 – 2004 | 9 | 3 |
Using only completed decades (1941 – 2000), calculate the least squares line for the number of major hurricanes expected based on the total number of hurricanes. (Round your answers to three decimal places.)
Using only completed decades (1941 – 2000), calculate the least squares line for the number of major hurricanes expected based on the total number of hurricanes. (Round your answers to three decimal places.)
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