2. A person’s blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter) 1/10 of a liter) of blood. After a 12- hour fast, the random variable x will have a distribution that is approximately normal with mean µ = 85 and standard deviation ợ = 25 (Source: Diagnostic Tests with Nursing Implications, edited by S. Loeb, Springhouse Press). Note: After 50 years of age, both the mean and standard deviation tend to increase. What is the probability that, for an adult (under 50 years old) after 12- hour fast? (d) X is greater than 140 (borderline diabetes starts at 140)? (e) Find the 85th percentile.
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!
2. A person’s blood glucose level and diabetes are closely related. Let x be a random variable measured
in milligrams of glucose per deciliter) 1/10 of a liter) of blood. After a 12- hour fast, the random variable x
will have a distribution that is approximately normal with mean µ = 85 and standard deviation ợ = 25
(Source: Diagnostic Tests with Nursing Implications, edited by S. Loeb, Springhouse Press). Note: After 50
years of age, both the mean and standard deviation tend to increase. What is the
(under 50 years old) after 12- hour fast?
(d) X is greater than 140 (borderline diabetes starts at 140)?
(e) Find the 85th percentile.
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