Suppose that the amount of caffeine (in milligrams) in an 16 fluid ounce energy drink can be modeled by the Normal Distribution with a mean of 250 mg and a standard deviation of 70 mg. What is the caffeine content of the 70th percentile of energy drinks? Interpret this value. The 70th percentile is 287 mg. This means that 70% of energy drinks will have caffeine less than or equal to 287 mg. The 70th percentile is 287 mg. This means that 70% of energy drinks will have caffeine greater than or equal to 287 mg. The 70th percentile is 213 mg. This means that 70% of energy drinks will have caffeine greater than or equal to 213 mg. The 70th percentile is 213 mg. This means that 70% of energy drinks will have caffeine less than or equal to 213 mg.
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!
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