If the random variable X is uniformly distributed between 40 and 60, then P(35 $\le$X $\le$ 45) is:
A) 1.0 .
B) 0.5 .
C) 0.25 .
D) 0.0 .

Question

If the random variable X is uniformly distributed between 40 and 60, then P(35 $\le$X $\le$ 45) is: 
A) 1.0 . 
B) 0.5 . 
C) 0.25 . 
D) 0.0 .

Quizplus · Accepted Answer

The probability density function of a uniform distribution is constant over the interval of support. In this case, the interval of support is [40, 60], so the probability density function is:```f(x) = 1 / (60 - 40) = 1 / 20 = 0.05```Therefore, the probability of X being between 35 and 45 is:```P(35 ≤ X ≤ 45) = ∫[35, 45] f(x) dx = ∫[35, 45] 0.05 dx = 0.05 * (45 - 35) = 0.25```

If the Random Variable X Is Uniformly Distributed Between 40 ≤\le≤

If the Random Variable X Is Uniformly Distributed Between 40 $\le$