Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-3. The probability that X will take on a value of at least 26 is
A)0.000
B)0.125
C)0.250
D)1.000

Question

Quizplus · Accepted Answer

The probability that X will take on a value of at least 26 is equal to the area under the probability density function from 26 to 28. Since X has a uniform distribution, the probability density function is constant over the interval from 20 to 28 and equal to 1/(28-20) = 1/8. Therefore, the probability that X will take on a value of at least 26 is:
P(X ≥ 26) = ∫26 to 28 (1/8)dx = (1/8)∫26 to 28 dx = (1/8)(28-26) = 0.25 or 1/4 or 25%.

Hence, the answer is C (0.250).

Exhibit 6-3 Consider the Continuous Random Variable X, Which Has a Uniform