11.31 Runners. In a study of exercise, a large group of malerunners walk on a tr
ID: 3262941 • Letter: 1
Question
11.31 Runners. In a study of exercise, a large group of malerunners walk on a treadmill for 6 minutes. After this exercise, theirheart rates vary with mean 8.8 beats perfive seconds and standard deviation 1.0beats per five seconds. This distributiontakes only whole-number values, so it iscertainly not Normal.(a) Let x be the mean number of beatsper five seconds after measuring heartrate for 12 five-second intervals (aminute). What is the approximate distribution of x according to the centrallimit theorem?(b) What is the approximate probability that x is less than 8?(c) What is the approximate probability that the heart rateof a runner is less than 100 beats per minute? (Hint: Restatethis event in terms of x.) 11.31 Runners. In a study of exercise, a large group of malerunners walk on a treadmill for 6 minutes. After this exercise, theirheart rates vary with mean 8.8 beats perfive seconds and standard deviation 1.0beats per five seconds. This distributiontakes only whole-number values, so it iscertainly not Normal.(a) Let x be the mean number of beatsper five seconds after measuring heartrate for 12 five-second intervals (aminute). What is the approximate distribution of x according to the centrallimit theorem?(b) What is the approximate probability that x is less than 8?(c) What is the approximate probability that the heart rateof a runner is less than 100 beats per minute? (Hint: Restatethis event in terms of x.)Explanation / Answer
Ans:
a)Accordinng to central limt theorm ot Normal distribution
b)z=(8-8.8)/(1/sqrt(12))=-0.8*3.464=-2.77
P(z<-2.77)=0.0028
b)x=100 beats per minutes=100/12 per 5 sec=8.33
z=(8.33-8.8)/(1/sqrt(12))=-0.47*3.464=-1.628
P(z<-1.628)=0.0518
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