Suppose that 90% of Narnians are children, that Narnian children have normally distributed BMIs with a mean of 25 kg/m^2 and variance of 64 (kg/m^2)^2 , and that Narnian adults have normally distributed BMIs with a mean of 30 kg/m^2 and variance of 100 (kg/m^2)^2 . WHO currently categorizes BMIs greater than 30 as obese. a. What is the prevalence of obesity among Narnian children? b. What is the prevalence of obesity among Narnian adults? c. What is the overall prevalence of obesity among Narnians?
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!
Suppose that 90% of Narnians are children, that Narnian children have
a. What is the prevalence of obesity among Narnian children?
b. What is the prevalence of obesity among Narnian adults?
c. What is the overall prevalence of obesity among Narnians?
d. Are age and obesity statistically independent in Narnia?
e. What proportion of Narnians are obese children?
f. What proportion of obese Narnians are children?
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