The graph of the probability density function of a random variable $$\(X\)$$ is symmetrical about the line $$\(x=4\)$$. Given that $$\(\mathrm{P}(X<5)=\frac{20}{27}\)$$, find P(3<X<5)

6.3.1 understand the concept of a continuous random variable, and recall and use properties of a probability density function (For density functions defined over a single interval only; the domain may be infinite,.)

6.3.2 use a probability density function to solve problems involving probabilities, and to calculate the mean and variance of a distribution. (Including location of the median or other percentiles of a distribution by direct consideration of an area using the density function.) (Explicit knowledge of the cumulative distribution function is not included.)