5.97 A random walk. A particle moves along the line in a random walk. That is, the particle starts at the origin (position 0) and moves either right or left in independent steps of length 1. If the particle moves to the right with probability 0.6, its movement at the ith step is a random variable X_i with distribution

P(X_i = 1) = 0.6

P(X_i = −1) = 0.4

The position of the particle after k steps is the sum of these random movements,

Y = X₁ + X₂ + · · · + X_k

Use the central limit theorem to find the approximate probability that the position of the particle after 500 steps is at least 200 to the right.