SOLUTION: 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. Fin

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Question 1137391: 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
(a) at most 8.8 liters;
(b) more than 7.4 liters but less than 9.5 liters;
(c) at least 8.5 liters.

Please show he solution on how you get it. Thanks.
Answer by ikleyn(52752) About Me  (Show Source):
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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
(a) at most 8.8 liters;
(b) more than 7.4 liters but less than 9.5 liters;
(c) at least 8.5 liters.

Please show he solution on how you get it. Thanks.
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Each time the answer is the ratio of the lengths of the two corresponding measuring intervals.


(a)  The condition means that the volume V is in the interval  7 <= V <= 8.8 liters.

     The length of the possible outcome interval is  8.8 - 7 = 1.8 liters.

     The ratio to the base interval of 10-7 = 3 liters  is  1.8%2F3 = 0.6,

     so the probability  is  P = 0.6.



(b)  The condition means that the volume V is in the interval  7.4 <= V <= 9.5 liters.

     The length of the possible outcome interval is   9.5 - 7.4 = 2.1 liters.

     The ratio to the base interval of  10-7 = 3 liters  is  2.1%2F3 = 0.7,

     so the probability  P = 0.7.



(c)  The condition means that the volume V is in the interval  8.5 <= V <= 10 liters.

     The length of the possible outcome interval is   10 - 8.5 = 1.5 liters.

     The ratio to the base interval of  10-7 = 3 liters  is  1.5%2F3 = 0.5,

     so the probability  P = 0.5 in this case.

Solved, answered and completed.