The amount of gasoline in gallons sold by three different gas stations during one day is given by the independent random variables X1,X2 and X3, each with a normal distribution. X1 has mean μ1 = 600 and standard deviation σ1 = 55; X2 has mean μ2 = 800 and standard deviation σ2 = 75; X3 has mean μ3 = 850 and standard deviation σ3 = 100. Suppose the prices per gallon are $3.10, $3.20, and $2.90 for X1, X2, and X3 respectively a) Find the expected combined revenue of the gas stations for a given day. b) Find the standard deviation of this combined revenue.
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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