Question

Using the following uniform density​ curve, answer the question. A coordinate system has a horizontal x-axis labeled from 0 to 8 in increments of 1 and a vertical P(x)-axis labeled from 0 to 0.125 in increments of 0.125. A horizontal line segment extends from (0, 0.125) to (8, 0.125). A vertical line segment extends from (8, 0.125) to (8, 0). What is the probability that the random variable has a value greater than​ 5?

Answer 1

Answer:

0.375

Step-by-step explanation:

Given that a coordinate system has a horizontal x-axis labeled from 0 to 8 in increments of 1 and a vertical P(x)-axis labeled from 0 to 0.125 in increments of 0.125. A horizontal line segment extends from (0, 0.125) to (8, 0.125). A vertical line segment extends from (8, 0.125) to (8, 0).

i.e. we can say X follows a uniform distribution with

p(x) = 0.125, for $0\leq x\leq 8$

This is a continuous uniform distribution

Required probability

= the probability that the random variable has a value greater than​ 5

= $\int\limits^8_5 {0.125} \, dx \\= 0.125(8-5)\\= 0.375$