Chapter 9.3 #13

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.

  1. Find the mean and variance of the average velocity of the particles.
n <- 10^20
mean <- 0 
var <-  1/n

cat("Mean :", mean)
## Mean : 0
cat("\nVariance :", var)
## 
## Variance : 1e-20
  1. What is the probability that the average velocity is ≥ 10−9 cm/sec
m <- 1e-9
Z <- m / sqrt(var)


prob <- 1 - pnorm(Z)

cat("Probability that the average velocity is >= 10^-9 cm/sec:", prob)
## Probability that the average velocity is >= 10^-9 cm/sec: 0