Suppose you toss a fair coin n times and record the number of heads that land. Assume that n is large and approximate the discrete random variable X with a continuous random variable that is normally distributed with μ = n/2 and σ = √n/2. If n = 400, find the given probabilities.

a. P(190 ≤ X < 210) 

b. P(X < 170)

c. P(X > 220) 

d. P(X = 300)