If x,the time (in minutes)to complete an oil change job at a certain auto service station,is uniformly distributed over the interval 20 to 30,inclusively (20 $\le$ x $\le$ 30),then the probability that an oil change job is completed in 25 to 28 minutes,inclusively,i.e. ,P(25 $\le$ x $\le$ 28)is ___.
A)0.250
B)0.500
C)0.300
D)0.750
E)81.000

Question

Quizplus · Accepted Answer

Since the time for completing an oil change job is uniformly distributed, the probability of completing the job in any interval within the range of 20 to 30 minutes is the same. Therefore, the probability of completing the job in the interval of 25 to 28 minutes is the ratio of the length of this interval to the length of the entire range (which is 10 minutes):
P(25 ≤ x ≤ 28) = (28 - 25) / (30 - 20) = 3 / 10 = 0.3

Therefore, the best choice is C) 0.300.

If X,the Time (In Minutes)to Complete an Oil Change Job ≤\le≤

If X,the Time (In Minutes)to Complete an Oil Change Job $\le$