You're looking for the 15th percentile of a normal distribution with µ = 242 and σ = 13, which is to say you want to find x * such that
P(X ≤ x *) = 0.15
Transform the wait-time random variable X to Z, which follows the standard normal distribution with mean 0 and s.d. 1 :
Z = (X - µ) / σ → X = µ + σ Z = 242 + 13 Z
Now,
P(X ≤ x *) = P(242 + 13 Z ≤ x *) = P(Z ≤ (x * - 242)/13) = 0.15
Use a calculator (something with an inverse CDF function) or Z-table to look up the z-score, z = (x * - 242)/13, associated with a probability of 0.15. You would find that
z = (x * - 242)/13 ≈ -1.03643
Solve for x * :
x * ≈ 242 + 13 (-1.03643) ≈ 228.526 ≈ 229
