Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 2$ and $d = 10$. Find the value of a that makes the following probability statement true: $P ( 2.5 \leq x \leq a ) = 0.5$.
A) 6
B) -0.8
C) 6.5
D) 3

Question

Quizplus · Accepted Answer

The uniform distribution has a constant probability over the interval [c, d]. The length of the interval is $d - c = 10 - 2 = 8$. To find $a$ such that $P(2.5 \leq x \leq a) = 0.5$, we need the interval length $(a - 2.5)$ to be half of the total interval length, i.e., $0.5 \times 8 = 4$. Thus, $a - 2.5 = 4$, giving $a = 6.5$.

Suppose xxx Is a Random Variable Best Described by a Uniform Probability

Suppose $x$ Is a Random Variable Best Described by a Uniform Probability