15.34 Runners. In a study of exercise, a large group of male runners walk on a treadmill for six minutes. After this exercise, their heart rates vary with mean 8.8 beats per five seconds and standard deviation 1.0 beats per five seconds. The researcher records the number of heartbeats per five seconds for each runner over a period of time. This distribution takes only whole-number values, so it is certainly not Normal. a. Let x be the mean number of beats per five seconds after measuring heart rate for 24 five-second intervals (two minutes). What is the approximate distribution of x according to the central limit theorem? b. What is the approximate probability that x is less than 8? c. What is the approximate probability that the heart rate of a runner is less than 100 beats per minute? (Hint: Restate this event in terms of x.)