  We study the time delay of reflected and transmitted waves in 1D disordered
media with high transmission. Highly transparent and translucent random media
are found in nature or can be synthetically produced. We perform numerical
simulations of microwaves propagating in disordered waveguides to show that
reflection amplitudes are described by complex Gaussian random variables with
the remarkable consequence that the time-delay statistics in reflection of 1D
disordered media are described as in random media in the diffusive regime. For
transmitted waves, we show numerically that the time delay is an additive
quantity and its fluctuations thus follow a Gaussian distribution. Ultimately,
the distributions of the time delay in reflection and transmission are physical
illustrations of the central limit theorem at work.
