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(5 ≤ X ≤ 11)?
A)0.167
B)0.833
C)1.000
D)0.000

Question

Quizplus · Accepted Answer

To find P(5 ≤ X ≤ 11), we first need to determine the range of X. Since X is uniformly distributed over the interval 4 to 10, its range is 10 - 4 = 6.

Next, we need to determine the probability that X falls within the given range. This can be done using the formula for the uniform distribution:

P(a ≤ X ≤ b) = (b - a) / (max - min)

Where a and b are the endpoints of the range of interest, and max and min are the maximum and minimum possible values of X.

In our case, a = 5, b = 10 (since X cannot exceed 10), max = 10, and min = 4. Substituting these values into the formula, we get:

P(5 ≤ X ≤ 10) = (10 - 5) / (10 - 4) = 5 / 6 ≈ 0.833

Therefore, the answer is B.