Physicists say that particles in the long tube are constantly moving back as well as forth along the tube, each with the velocity Vk(in cm/sec) at any given moment that is normally distributed, with mean mu=0 and variance sigma^2=1. Assume there are 10^20 particles in the tube
(a) Determine the mean and variance of the average velocity of the particles
(b) Determine the probability that the average velocity is more than or equal to 10^-9 cm/sec