In a study of exercise, a large group of male runners walk on a treadmill for si

Question

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 8.7 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. (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 centra limit theorem? mean standard deviation beats per five seconds beats per five seconds (b) What is the approximate probabity that x is less than 8? (c) What is the approximate probability that the heart rate of a runner is less than 95 beats per minute? (Hint: Restate this event in terms of x.) You may need to use the appropriate Appendix Table to answer this question

Explanation / Answer

a) mean=8.7

std deviation =1.1/(24)1/2 =0.2245

b)

P(Xbar<8)=P(Z<(8-8.7)/0.2245)=P(Z<-3.1175)=0.0009

c)

as 1 minute =12 of 5 second interval

hence sample mean =95/12=7.9167

std deviation=1.1/(12)1/2 =0.3175

hence probability=P(X<7.9167)=P(Z<(7.9167-8.7)/0.3175)=P(Z<-2.4669)=0.0068

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