Suppose that at a gas station the daily demand for regular gasoline is normally distributed with a mean of 1000 gallons and a standard deviation of 100 gallons. The station manager has just opened the station for business and there is exactly 2300 gallons of regular gasoline in storage. The next delivery is scheduled later tomorrow at the close of business. (a) Let X1 and X2 denote the demand of today and tomorrow, respectively. Let X = X1 + X2. Find the distribution of X. (b) Find the probability that the manager will have enough regular gasoline to satisfy today’s and tomorrow’s demand.
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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