There is no 'random number'. Perhaps you mean 'a series of (uniformly/normally distributed?) random numbers between 0 and k'? For a normally distributed series

There is no 'random number'. Perhaps you mean 'a series of (uniformly/normally distributed?) random numbers between 0 and k'? For a normally distributed series of numbers make a jump and report the length (in milimeters). You will produce a series normally distributed around your average jumping length.