A coffee - dispensing machine used in cafeterias is set to dispense coffee with an average fill of 230 ml and standard deviation of 10 ml per cup. Assume that the volume dispensed is normally distributed. (a) for a randomly selected selected cup dispensed by machine, what is the probability that: I)the cup is filled for more than 235 ml? (II) the cup is filled between 235 ml and 245 ml? (III) the cup is less than 220 ml full. (b) if the company supplying the coffee wants only 15% of cups to exceed a given fill level, what level of fill ( in ml) does this correspond to? (c) what must the mean fill level (in ml) be set to in order to ensure that no more than 10% of cups are filled to less than 220 ml?
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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