Respuesta :
Answer:
a) 60% probability that on a given day the amount of coffee dispensed by this machine will be at most 8.8 liters.
b) 70% 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
c) 50% probability that on a given day the amount of coffee dispensed by this machine will be at least 8.5 liters
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
The probability of X being higher than x is:
[tex]P(X > x) = 1 - \frac{x - a}{b-a}[/tex]
The probability of X being between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
For this problem, we have that:
[tex]a = 7, b = 10[/tex]
(a) at most 8.8 liters;
[tex]P(X \leq 8.8) = \frac{8.8 - 7}{10 - 7} = 0.6[/tex]
60% probability that on a given day the amount of coffee dispensed by this machine will be at most 8.8 liters.
(b) more than 7.4 liters but less than 9.5 liters;
[tex]P(7.4 \leq X \leq 9.5) = \frac{9.5 - 7.4}{10 - 7} = 0.7[/tex]
70% 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
(c) at least 8.5 liters.
[tex]P(X > 8.5) = 1 - \frac{8.5 - 7}{10 - 7} = 0.5[/tex]
50% probability that on a given day the amount of coffee dispensed by this machine will be at least 8.5 liters
