Question

The daily amount of coffee, in liters, dispensedby a machine located in an airport lobby is a randomvariable X having a continuous uniform distributionwith A = 7 and B = 10. Find the probability thaton a given day the amount of coffee dispensed by thismachine will be(a) at most 8.8 liters;

Answer 1

Answer:

The probability that the machine will dispense at most 8.8 liters is 0.60

Step-by-step explanation:

A uniform distribution, also called a rectangular distribution, is a probability distribution that has constant probability.

The distribution is given by:

f(x)={$\frac{1}{B-A}$⇒A≤x≤B; 0 ⇒ elsewhere}

Hence,

P(x≤8.8)=$\int\limits^{8.8}_7 {\frac{1}{B-A} } \, dx =\int\limits^{8.8}_7 {\frac{1}{10-7} } \, dx =\int\limits^{8.8}_7 {\frac{1}{3} } \, dx=\frac{1}{3}(8.8-7)=\frac{1}{3}(1.8)=0.6$

The probability that the machine will dispense at most 8.8 liters is 0.60