What is the missing value for the P(1) in the probability distribution below? P(x) 0.285 1 0.130 0.492 v 2 correct 3 0.093 HINT: The probabilities need to add up to 1. What is the mean of the distribution above? DO NOT ROUND YOUR ANSWER u = 1.393 correct What is the standard deviation above? DO NOT ROUND YOUR ANSWER O = 0.9138875 According to the empirical rule, what are the lowest and highest reasonable x values for the distribution above? ROUND YOUR ANSWERS TO 3 DECIMAL PLACES Highest reasonable value: 4.385 x * incorrect Lowest reasonable value: -1.599 ×
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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