Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean ? = 81 and estimated standard deviation ? = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed. Explain what this might imply if you were a doctor or a nurse. A. The more tests a patient completes, the weaker is the evidence for excess insulin. B. The more tests a patient completes, the weaker is the evidence for lack of insulin. C. The more tests a patient completes, the stronger is the evidence for lack of insulin. D. The more tests a patient completes, the stronger is the evidence for excess insulin.
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!
Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with
Explain what this might imply if you were a doctor or a nurse.
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