15.E.033. My Notes Ask Your In a study of exercise, a large group of male runner

Question

15.E.033. My Notes Ask Your 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. This distribution takes only whole-number values, so it is certainly not Normal. (Round your answers to four decimal places) (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? mean standard deviation beats per five seconds beats per five seconds (b) What is the approximate probability that is less than 8 (c) what is the approximate probability that the heart rate of a runner is less than 96 beats per minute? (Hint: Restate this event in terms of x.) You may need to use the appropriate Appendix Table to answer this question. eBook

Explanation / Answer

a) mean =8.8

std deviaiton =1.0/(24)1/2 =0.2041

b) P(Xbar<8)=P(Z<(8.-8.8)/0.2041)=P(Z<-3.92)=0.0000

c)

here as there are 12 5 second period in 1 minute

here mean =96/12 =8

and std deviation=1/(12)1/2 =0.2887

hence P(Xbar<8)=P(Z<(8.-8.8)/0.2887)=P(Z<-2.77)=0.0028

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