Question

Find the value of c for which P(x < c) = 0.7.

Answer 1

Uniform distribution $U(a, b)$

$$x\in [a, b]$$

$$f(x; a, b) = \begin{cases} \dfrac{1}{b-a} &a \leq x \leq b\\ 0 &\text{otherwise } \end{cases}$$

For $a \leq c\leq b$

$$P(x<c)=\dfrac{c-a}{b-a}$$

Given

$$P(x<c)=0.7$$

$$\dfrac{c-a}{b-a}=0.7$$

$$c=a+0.7(b-a)$$

$$c=0.3a+0.7b$$