If x, the time (in minutes)to complete an change job at 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 21.75 to 24.25 minutes, inclusively, i.e., P(21.75$\le$ x $\le$24.25)is __________________.
A)0.250
B)0.333
C)0.375
D)0.000
E)1.000

Question

Quizplus · Accepted Answer

The probability density function of a uniform distribution is constant over the interval. Therefore, the probability of an oil change job being completed in 21.75 to 24.25 minutes, inclusively, is equal to the length of this interval divided by the length of the entire interval. The length of the interval 21.75 to 24.25 is 24.25 - 21.75 = 2.5 minutes. The length of the entire interval 20 to 30 is 30 - 20 = 10 minutes. Therefore, the probability is 2.5 / 10 = 0.25.

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

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