A soft drink dispensing machine uses plastic cups that hold a maximum of 12 ounces. The machine varies. It is normally distributed with a standard deviation of s = 1 ounce. Use the Empirical Rule (68%-95%-99.7%) to answer these questions. set to dispense a mean of x = 10 ounces of liquid. The amount of liquid that is actually dispensed (a) What percentage of the cups contain between 10 and 11 ounces of liquid? % (b) What percentage of the cups contain between 8 and 10 ounces of liquid? % (c) What percentage of the cups spill over because 12 ounces of liquid or more is dispensed? % (d) What percentage of the cups contain between 8 and 9 ounces of liquid? %
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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