0.4 0.3 0.2 F 0.1 0.0 195 200 205 210 215 220 225 Cholesterol level (mg/dL) Relative frequency
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!
Cholesterol Levels. According to the National Health and Nutrition Examination Survey, published by the Centers for Disease Control and Prevention, the average cholesterol level for children between 4 and 19 years of age is 165 mg/dL. A pediatrician who tested the cholesterol levels of several young patients was alarmed to find that many had levels higher than 200 mg/dL. The following relativefrequency histogram shows the readings for some patients who had high cholesterol levels.
Use the graph to answer the following questions. Note that cholesterol levels are always expressed as whole numbers.
a. What percentage of the patients have cholesterol levels between 205 and 209, inclusive?
b. What percentage of the patients have levels of 215 or higher?
c. If the number of patients is 20, how many have levels between 210 and 214, inclusive?
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