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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.

Respuesta :

Nathanyel
 f(x) = 1/(10-7) = 1/3, 7<x<10. 
(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

The probability the coffee dispensed exceed 7.5L but less than 9.5L is 0.7

Data;

  • a = 7
  • b = 10

What is Probability?

Probability is the outcome of an event likely to happen. But Probability function is a function of a discrete random variable that gives the probability that the outcome associated with that variable.

Using the formula of uniform distribution, we can find the probability of the coffee dispensed does not exceed the range of 7.4L - 9.5L.

[tex]f(x) = \frac{1}{10-7} =\frac{1}{3} \\[/tex]

The probability can be calculated as

[tex]p(7.4\leq x\leq 9.5) = \frac{9.5 - 7.4}{3} = 0.7[/tex]

The probability the coffee dispensed exceed 7.5L but less than 9.5L is 0.7

Learn more on probability distribution here;

https://brainly.com/question/24756209

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