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 1.0 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 xaccording 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 97 beats per minute? (Hint: Restate this event in terms of x.)

Explanation / Answer

a)

mean = 8.7

standard deviation = 1/sqrt(24) = 0.2041

b)

z-value corresponding to x = 8 is (8-8.7)/0.2041 = -3.429

P( x < 8 ) = P(z < -3.429) = 0.000302

c)

heart rate less than 97 beats per minute imples less than 97/12 = 7.08333 beats per five seconds

z-value corresponding to x = 8.08333 is (8-8.08333)/0.2041 = -0.40828

P( x < 8.08333 ) = P(z < -0.40828) = 0.3415

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