The amount of regular unleaded gasoline purchased every week at a gas station near UCLA follows the normal distribution with mean 50,000 gallons and standard deviation 10,000 gallons. The starting supply of gasoline is 74,000 gallons, and there is a scheduled weekly delivery of 47,000 gallons. a. Find the probability that, after 11 weeks, the supply of gasoline wil be below 20,000 gallions. b. How much should the weekly delivery be so that after 11 weeks the probability that the supply is below 20,000 gallons is only 0.5%?
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!
The amount of regular unleaded gasoline purchased every week at a gas station near UCLA follows the
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