In a study of exercise, a large group of male runners walk on a treadmill for 8 minutes. After this…

In a study of exercise, a large group of male runners walk on a treadmill for 8 minutes. After this exercise, their heart rates vary with mean 8.5 beats per five seconds and standard deviation 1.1 beats per five seconds. This distribution takes only whole-number values, so it is certainly not Normal.

 

Let  be the mean number of beats per five seconds after measuring heart rate for 12 five-second intervals.  

What is the standard deviation (0.0001) of distribution of according to the central limit theorem? [removed] 

  beats per five seconds

 

What is the probability (0.0001) that  is less than 8? [removed]  

 

What is the probability (0.0001) that the heart rate of a runner is less than 105 beats per minute? [removed]  (Hint: restate this problem in terms of  per five seconds).