𝑋∼𝑁(54,8) Find the probability that 𝑥<42

Answer 1

Transform x to N(0,1) via z-score

z = (x - mean)/SD, where x = 42, mean = 54 and SD = 8

z = (42 - 54)/8 = -1.5

P(x < 42) = P(z < -1.5).

That probability can be found from standard normal probability distribution table