n Example 6 we used data from 1920 and projected to 2050 and found that the expected life span in the United States can be modeled as a function of the year of birth by L(x) = 8.7744 + 14.907 ln(x) where x is the number of years after 1900. Using data from 1920 to 1989, the model ℓ(x) = 11.616 + 14.144 ln(x) where x is the number of years after 1900, predicts expected life span as a function of birth year. Use both models to predict the life spans for people born in 2006 and in 2022. (Round your answers to two decimal places.) model L: 2006 years model L: 2022 years model ℓ: 2006 years model ℓ: 2022 years Did adding data from 1990 to 2050 give predictions that were quite different from or very similar to predictions based on the model without that data? The additional data gave predictions that were quite different than (i.e., more than 5 years removed from) predictions based on the earlier model. The additional data gave predictions that were very similar to (i.e., within 5 years of) predictions based on the earlier model.
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!
In Example 6 we used data from 1920 and projected to 2050 and found that the expected life span in the United States can be modeled as a
where x is the number of years after 1900. Using data from 1920 to 1989, the model
where x is the number of years after 1900, predicts expected life span as a function of birth year. Use both models to predict the life spans for people born in 2006 and in 2022. (Round your answers to two decimal places.)
| model L: 2006 | years |
| model L: 2022 | years |
| model ℓ: 2006 | years |
| model ℓ: 2022 | years |
Did adding data from 1990 to 2050 give predictions that were quite different from or very similar to predictions based on the model without that data?
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