THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The continuous random variable X is uniformly distributed over the interval 4 to 10.
-What is P(6 ≤ X ≤ 8)?
A)0.167
B)0.333
C)0.567
D)0.833

Question

Quizplus · Accepted Answer

Since X is uniformly distributed, the probability of any value in the interval 4 to 10 is equally likely. The total length of the interval is 10-4=6, and the length of the subinterval 6 ≤ X ≤ 8 is 8-6=2. Therefore, the probability of X being in the subinterval 6 ≤ X ≤ 8 is equal to the length of the subinterval divided by the total length of the interval, which is 2/6 or 1/3, so the answer is B.