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

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

Explanation:

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

The distribution is given by:

f(x)={
`(1)/(B-A)`⇒A≤x≤B; 0 ⇒ elsewhere}

Hence,

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

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