Physicists say that particles in a long tube are constantly moving back and forth along the tube, each with a velocity Vk (in cm/sec) at any given moment that is normally distributed, with mean μ=0 and variance σ2=1. Suppose there are 1020 particles in the tube.
(a) Find the mean and variance of the average velocity of the particles.
(b) What is the probability that the average velocity is ≥10−9 cm/sec?