The mean serum cholesterol level of a large population of overweight children is 220 milligrams per deciliter (mg/dl), and the standard deviation is 16.3 mg/dl. Assume the serum cholesterol level variable is normally distributed. a. If 1 child is selected, find the probability that the mean will be between 216 and 224 mg/dl. b. If a random sample of 12 overweight children is selected, find the probability that the mean will be between 216 and 224 mg/dl.
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!
Central Limit Theorem
The
a. If 1 child is selected, find the
b. If a random sample of 12 overweight children is selected, find the probability that the mean will be between 216 and 224 mg/dl.
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