The heights of American men are known to be normally distributed with a mean of 68.5 inches and a standard deviation of 2.2 inches.

Pictures required for first two parts.


Part A: What is the probability that a randomly selected American man is taller than 72.5 inches?


Part B: What is the probability that the average height of 35 randomly selected American men is taller than 72.5 inches?


Part C: Would your answers to the above questions change if we did not know whether or not the heights of American men were normally distributed? Explain your reasoning.