Greenstone Coffee is experiencing financial pressures due to increased competition for its numerous urban coffee shops. Total sales revenue has dropped by 15% and the company wishes to establish a sales monitoring process to identify shops that are underperforming. Historically, the daily mean sales for a shop have been $11,500 with a variance of 4,000,000. Their monitoring plan will take a random sample of 5 days’ sales per month and use the sample mean sales to identify shops that are underperforming. Establish the lower limit sales such that only 5% of the shops would have a sample sales mean below this value.
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!
Greenstone Coffee is experiencing financial pressures due to increased competition for its numerous urban coffee shops. Total sales revenue has dropped by 15% and the company wishes to establish a sales monitoring process to identify shops that are underperforming. Historically, the daily
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