Severely obese persons (BMI ≥ 40) have a greatly increased risk of diabetes, heart disease, and many other ailments that are very expensive to treat. The table gives the percent of Americans who are severely obese from the year 1990 and projected to 2030. Year 1990 2000 2010 2015 2020 2025 2030 % Severely Obese 0.8 2.2 4.9 6.4 7.9 9.5 11.1 (a) Find an exponential function that models the data, with x equal to the number of years after 1990 and y equal to the percent. (Round your numerical values to three decimal places.) y = (b) Does the unrounded model overestimate or underestimate the percent of severely obese Americans in 2020? (c) According to the unrounded model, in what year are 11.1% of Americans expected to be severely obese?
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!
Severely obese persons (BMI ≥ 40) have a greatly increased risk of diabetes, heart disease, and many other ailments that are very expensive to treat. The table gives the percent of Americans who are severely obese from the year 1990 and projected to 2030.
| Year | 1990 | 2000 | 2010 | 2015 | 2020 | 2025 | 2030 |
|---|---|---|---|---|---|---|---|
| % Severely Obese |
0.8 | 2.2 | 4.9 | 6.4 | 7.9 | 9.5 | 11.1 |
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