The cholosterol levels of men in the United States are normally distributed, with a mean 215 milligrams per deciliter and a standard deviation 25 milligrams per deciliter. 1. If a man is randomly selected, what is the probability that his cholesterol level is more than 245? 2. based on your answer #1, would you consider it unusual for a man to have a cholesterol level of 245? 3. What cholosterol level cuts off the lowest 10% of levels?
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!
The cholosterol levels of men in the United States are
1. If a man is randomly selected, what is the
2. based on your answer #1, would you consider it unusual for a man to have a cholesterol level of 245?
3. What cholosterol level cuts off the lowest 10% of levels?
1.
The cholesterol levels of men are normally distributed, with a mean 215 milligrams per deciliter and a standard deviation 25 milligrams per deciliter.
The z score for cholesterol level 245 is,
The probability of z less than 1.2 can be obtained using the excel formula “=NORM.S.DIST(1.2,TRUE)”. The probability value is 0.8849.
The probability that his cholesterol level is more than 245 is,
Thus, the probability that man's cholesterol level is more than 245 is 0.1151.
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