Consider a probability distribution given by the density function \(𝑃(𝑥)\).…

Consider a probability distribution given by the density function $𝑃(𝑥)$.

$P(x) = \begin{cases} Cx^2, & \text{for } 1 \leq x \leq 4 \\ 0, & \text{for } x < 1 \text{ or } x > 4 \end{cases}$

The probability that $x$ lies between 2 and 3, i.e., $𝑃(2 ≤ 𝑥 ≤ 3)$ is __________. (rounded off to three decimal places)