The actual amount of coffee (in grams) in a 230-gramjar filled by a certain machine is a random variable whoseprobability density is given by f(x) =⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩0 for x F 227.515 for 227.5 < x < 232.50 for x G 232.5 Find the probabilities that a 230-gram jar filled by thismachine will contain(a) at most 228.65 grams of coffee;(b) anywhere from 229.34 to 231.66 grams of coffee;(c) at least 229.85 grams 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!
jar filled by a certain machine is a random variable whose
probability density is given by
⎧
⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎩
0 for x F 227.5
1
5 for 227.5 < x < 232.5
0 for x G 232.5
machine will contain
(a) at most 228.65 grams of coffee;
(b) anywhere from 229.34 to 231.66 grams of coffee;
(c) at least 229.85 grams of coffee.
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