This exercise, their heart rates vary with mean 8.8 beats per five seconds and s

Question

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. (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?

Explanation / Answer

a)as per central limit theorum that would be approximately normal

b)std error =std deviation/(n)1/2 =0.2041

and hence P(X<8) =P(Z<(8-8.8)/0.2041) =P(Z<-3.9192)=0.00004

c)per minute value of mean =8.8*12=105.6

and std deviation =1*(12)1/2 =3.4641

hence P(Z<100)=P(Z<100-105.6)/3.4641)=P(Z<-1.6166)=0.053

P(X<8)=

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