An automatic dispensing machine dispenses a certain beverage into a 20 ounce cup. Let X be the amount dispensed by the machine where X is Normal with a mean of 19.8, and a standard deviation of 0.9. Let Y be the size of the 20-ounce cup, where Y is Normal with a mean of 20.1 and a standard deviation of 0.7. What is the probability that a randomly selected cup automatically filled by this machine will overflow? We can assume that X and Y are independent. A. 40.9% B. 39.74% C. 60.26% D. 59.1%
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We want to find the probability that X > Y, which means the amount dispensed (X) is greater than the cup size (Y). Show more…
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