Question

If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, then what is the probability that an oil change job is completed in less than or equal to 22 minutes?

Answer 1

The value is
`P(X \le 22) = 0.2`

Explanation:

From the question we are told that

The lower limit of the interval is
`a = 20`

The upper limit of the interval is
`b = 30`

Generally the cumulative distribution function for uniform distribution is mathematically represented as

`F(x) = \left \{ {{0 \ \ \ \ \ \ \ \ \ \ \ for x < a } \atop {(x - a)/(b-a) \ \ \ \ \ \ for  a \le x \le b }} \atop { 1 \ \ \ \ \ \ \ \ \ \ \  for  x >  b}\right.`

Generally the probability that an oil change job is completed in less than or equal to 22 minutes is mathematically represented as

`P(X \le 22) = (22 - 20)/(30 - 20 )`

=>
`P(X \le 22) = 0.2`