A study by M. Chen et al. titled "Heat Stress Evaluation and Worker Fatigue in a Steel Plant" (American Industrial Hygiene Association, Vol. 64, pp. 352-359) assessed fatigue in steel-plant workers due to heat stress. If the mean post-work heart rate for casting workers equals the normal resting heart rate of 72 beats per minute (bpm), find the probability that a random sample of 29 casting workers will have a mean post-work heart rate exceeding 78.3 bpm. Assume that the population standard deviation of post-work heart rates for casting workers is 11.2 bpm. State any assumptions that you are making in solving this problem.