A patient visits her doctor with concerns about her blood pressure. If the systolic blood pressure exceeds 150, the patient is considered to have high blood pressure and medication may be prescribed. The problem is that there is a considerable variation in a patient’s systolic blood pressure readings during a given day. If a patient’s systolic readings during a given day have a normal distribution with a mean of 155 and a standard deviation of 20, what is the probability that a single measurement will fail to detect that the patient has high blood pressure? If six measurements are taken at various times during the day, what is the probability that the average blood pressure reading will be less than 150 and hence fail to indicate that the patient has a high blood pressure problem? How many measurements would be required so that the probability of failing to detect high blood pressure is no more than 5%
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!
A patient visits her doctor with concerns about her blood pressure. If the systolic blood pressure exceeds 150, the patient is considered to have high blood pressure and medication may be prescribed. The problem is that there is a considerable variation in a patient’s systolic blood pressure readings during a given day.
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- If a patient’s systolic readings during a given day have a
normal distribution with a mean of 155 and a standard deviation of 20, what is theprobability that a single measurement will fail to detect that the patient has high blood pressure? - If six measurements are taken at various times during the day, what is the probability that the average blood pressure reading will be less than 150 and hence fail to indicate that the patient has a high blood pressure problem?
- How many measurements would be required so that the probability of failing to detect high blood pressure is no more than 5%
- If a patient’s systolic readings during a given day have a
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