A coffee machine discharges an average of μ=7.1 ounces when you press the discharge button. Assume the ounces of fill, X, are normally distributed with standard deviation of 0.3 ounce. a. What percentage of the cups (how often) will overflow, if we use the machine to fill 7.7 ounce cups? (Hint: use empirical rule and explain your answer.) b. What percentage of the cups will be filled at most with 7.1 ounces of coffee?
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!
A coffee machine discharges an average of μ=7.1 ounces when you press the discharge button. Assume the ounces of fill, X, are
a. What percentage of the cups (how often) will overflow, if we use the machine to fill 7.7 ounce cups? (Hint: use
b. What percentage of the cups will be filled at most with 7.1 ounces of coffee?
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