First as you have typed the question there is no answer as you have not specified a distribution. But lets assume you mean uniformly distributed between 300 and 480 seconds.

Probability that travelling time is less than 435 is:

integral (p(x) dx, x=-inf,435) = integral (1/180) dx, x=300,435)

as p(x)=(1/180) for x in (300, 480), and 0 otherwise.

integral (p(x) dx, x=-inf, 435) = integral (1/180) dx, x=300, 435)

............................. ..=(1/180) (435-300)=135/180 =0.75

By definition the mean:

m = integral (x p(x) dx, x=-inf, inf) = integral (x/180 dx, x=300, 480)

.............................. ........=480^2/360-300^2/360 =390.

The definition of SD:

s = sqrt(V),

V = integral ((x-m)^2 p(x) dx, x=-inf, inf)

which I will leave for you to do.

RonL