The number of gallons of paint that Home Depot sells in a given day is normally distributed with a mean of 219 gallons and a standard deviation of 27 gallons (I realize that the distribution is probably different for weekends compared to weekdays, but just assume everyday has the distribution). How many gallons of paint have to be sold in a given day in order for that day to be in the top 10% of the highest number of gallons sold? (please round your answer to 2 decimal places)
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 number of gallons of paint that Home Depot sells in a given day is
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