4. Milk is stocked at the grocery store each week. At the end of the week unsold milk is reduced in price by 50% of its selling price, and always sells for this lower price instantly. Weekly demand for milk is normally distributed with a mean of 200 gallons and standard deviation of 25 gallons. Each gallon of milk costs $1.75. Assuming a service level of 90% and that the store sells the milk for $3 per gallon, how many gallons should the store order this week?
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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