A continuous random variable is uniformly distributed between 150 and 250.

(a) What is the probability a randomly selected value will be greater than 230​?
(b) What is the probability a randomly selected value will be less than 170​?
(c) What is the probability a randomly selected value will be between 170 and 230​?

Respuesta :

Answer:

0.2,0.2,0.6

Step-by-step explanation:

Given that a continuous random variable is uniformly distributed between 150 and 250.

We know that a uniform distribution between (a,b) has pdf as

[tex]\frac{1}{b-a } \\=\frac{1}{100} ,150\leq x\leq 250[/tex]

a) the probability a randomly selected value will be greater than 230

=[tex]\frac{250-230}{250-150} \\=0.20[/tex]

b)  the probability a randomly selected value will be less than 170

=[tex]\frac{170-150}{250-150}\\=0.20[/tex]

c)  the probability a randomly selected value will be between 170 and 230​

=[tex]\frac{230-170}{250-150}\\=0.60[/tex]