Suppose you are given the following probability distribution: x f(x) 100 7% 150 16% 200 22% 250 30% 300 14% 350 8% 400 3% Determine the expected value. Determine the standard deviation. What is the probability that x is greater than 300? What is the probability that x is between 200 and 350 (inclusive)?
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!
Suppose you are given the following
x f(x)
100 7%
150 16%
200 22%
250 30%
300 14%
350 8%
400 3%
Determine the
Determine the standard deviation.
What is the probability that x is greater than 300?
What is the probability that x is between 200 and 350 (inclusive)?
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