Question
Desalination is the process of removing salt and other minerals from seawater to produce water that is drinkable. As potable drinking water sources dwindle, many
Desalination is the process of removing salt and other minerals from seawater to produce water that is drinkable. As potable drinking water sources dwindle, many countries are exploring sustainable ways to power desalination plants to supplement existing potable water supplies. However, some countries restrict the use of desalination plants to small, isolated communities that have no other access to fresh drinking water. In some cases, desalination plant are so small scale that they produce only 5,000 gallons of drinkable water each day. That's enough potable drinking water for about 500 households. Assume that the water consumption of a community on any particular day can be modeled by a continuous random variable, and the consumption between any two days are independent. The community consumes an average of 5,000 gallons of potable drinking water each day, but that the community's per-day drinking water consumption varies with a standard deviation of 1,000 gallons. The community's potable water reservoir initially contains 70,000 gallons of desalinated water and it's reliably supplanted with 5,000 gallons of additional desalinated water per day. What's the approximate probability that, after 60 days, the community reservoir stores less than 60,000 gallons of drinkable water? You shouldn't subdivide days into smaller time units or worry about the remote possibility that the reservoir is ever fully depleted. Your final answer can be left in terms of the function used to compute probabilities related to the Standard Normal distribution.
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