Question

If X ∼ N (4,25), then find P(x ≤ 4)

Answer 1

Given X ∼ N (4,25), 

μ = 4, `sigma^2` = 25    `therefore sigma` = 5

Let Z = `(x - μ)/sigma`

then Z ∼ N (0,1) 

P(X ≤ 4) = P `((x - μ)/sigma ≤ (4 - 4)/5)`

              = P (Z ≤ 0)

P(X ≤  4) = 0.5