Suppose a company rates its employees on a 1 to 4 scale with for being the highest rating and the following probability distribution describes the distribution of the ratings: 27% of the employees had a "4", 29% of the employees had a "3" 21% of the employees had a "2" and the remaining employees received a "1" rating. What is the expected value of the rating of a randomly chosen employee?
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 a company rates its employees on a 1 to 4 scale with for being the highest rating and the following
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