Physicists say that particles in a long tube are constantly moving back and forth along the tube, each with a velocity [math]V_k[/math] (in cm/sec) at any given moment that is normally distributed, with mean [math]\mu = 0[/math] and variance [math]\sigma^2 = 1[/math]. Suppose there are [math]10^{20}[/math] particles in the tube.

• Find the mean and variance of the average velocity of the particles.
• What is the probability that the average velocity is [math]{} \geq 10^{-9}[/math] cm/sec?