Question

A continuous random variable is uniformly distributed between 100 and 150.
a. What is the probability a randomly selected value will be greater than 130?

P(x > 130) = ______ . (Simplify your answer. Give as decimal.)

b. What is the probability a randomly selected value will be less than 120?

P(x < 120) = ______ . (Simplify your answer. Give as decimal.)

c. What is the probability a randomly selected value will be between 120 and 130?

P(120 < x < 130) = ______ . (Simplify your answer. Give as decimal.)

Answer 1

Solution :

Given that,

a = 100

b = 150

a) P(x > c) = (b - c) / (b - a)

P(x > 130) = (150 - 130) / (150 - 100)

P(x > 130) = 0.40

b) P(x < c) = (c - a) / (b - a)

P(x < 120) = (120 - 100) / (150 - 100)

P(x < 120) = 0.40

c) P(c < x < d) = (d - c) / (b - a)

P(120 < x < 130) = (130 - 120) / (150 - 100)

P(120 < x < 130) = 0.20