Clearly Z can take the values 1,..., 150. The value 150 is special: the plane is full if 150 or more people buy a ticket. Hence P(Z = 150) = P(X ≥ 150) = 51/200. For the other values we have P(Z = i)...

Clearly Z can take the values 1,..., 150. The value 150 is special: the plane is full if 150 or more people buy a ticket. Hence P(Z = 150) = P(X ≥ 150) = 51/200. For the other values we have P(Z = i) = P(X = i) = 1/200, for i = 1,..., 149. Clearly, here g(x) = min{150, x}.