The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable x having a continuous uniform distribution with a = 7 and b = 10. find the probability that on a given day the amount of coffee dispensed by this machine will be more than 7.4 liters but less than 9.5 liters.

Question

Mathematics

Hayley Ho

10 January, 12:40

The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable x having a continuous uniform distribution with a = 7 and b = 10. find the probability that on a given day the amount of coffee dispensed by this machine will be more than 7.4 liters but less than 9.5 liters.

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Chanel Huerta · Answer 1

f (x) = 1 / (10-7) = 1/3, 7
(a) P (at most 8.8 liters) = integral (7to8.8) f (x) dx = 1.8/3 = 0.6

(b) P (more than 7.4 liters but less than 9.5 liters) = integral (7.4 to9.5) f (x) dx = 2.1/3 = 0.7

(c) P (at least 8.5 liters) = integral (8.5 to10) f (x) dx = 1.5/3 = 0.5