In a study of hypertension and optimal treatment conducted by the National Heart Institute, 10,000 patients had a mean systolic blood pressure (BP), mu = 161 mm Hg and standard deviation, sigma = 25 mm Hg. Assume the systolic blood pressure is normally distributed. What is the probability of patients with a systolic blood pressure of more than 180 mm Hg? How many patients will have a systolic blood pressure of more than 180 mm Hg? What is the probability of patients with a systolic blood pressure between 145 and 160 mm Hg? If 60 random samples each of size 30 are drawn from this population, determine: I. the sampling distribution of the mean systolic blood pressure. II. the probability of the mean systolic blood pressure between 140 and 165 mm Hg.
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!
In a study of hypertension and optimal treatment conducted by the National Heart Institute, 10,000 patients had a mean systolic blood pressure (BP), mu = 161 mm Hg and standard deviation, sigma = 25 mm Hg. Assume the systolic blood pressure is
- What is the probability of patients with a systolic blood pressure of more than 180 mm Hg?
- How many patients will have a systolic blood pressure of more than 180 mm Hg?
- What is the probability of patients with a systolic blood pressure between 145 and 160 mm Hg?
- If 60 random samples each of size 30 are drawn from this population, determine:
I. the sampling distribution of the mean systolic blood pressure.
II. the probability of the mean systolic blood pressure between 140 and 165 mm Hg.
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