One study of mortality versus age used the following model to give the probability P of death from measles if contracted at age t years. P = 1/ 1 + 77.39e−0.08t Here we assume that t is at least 2. (a) What is the limiting value for this logistic function? Note: In other contexts, this would be known as the carrying capacity.(b) Explain in practical terms the meaning of the limiting value you found in part (a). The limiting value indicates that as age increases, the probability of death upon contracting measles at that age increases toward or %. (c) At what age does the model predict that mortality due to measles is 50%? (That is a value of 0.5 for P. Round your answer to two decimal places.) t =
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!
One study of mortality versus age used the following model to give the probability P of death from measles if contracted at age t years.
| 1/ |
| 1 + 77.39e−0.08t |
Here we assume that t is at least 2.
(b) Explain in practical terms the meaning of the limiting value you found in part (a).
(c) At what age does the model predict that mortality due to measles is 50%? (That is a value of 0.5 for P. Round your answer to two decimal places.)
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