Medical: Blood Glucose. 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 = 25. What is the probability that, for an adult after a 12 hour fast: a. x is less than 85? b. x is greater than 135 (borderline diabetes starts at 125)?
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!
Medical: Blood Glucose. 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 = 25. What is the probability that, for an adult after a 12 hour fast: a. x is less than 85? b. x is greater than 135 (borderline diabetes starts at 125)?
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