Question

ch 15 #12. (15.33) In a study of exercise, a large group of male runners walk on a treadmill for 8 minutes. After this exercise, their heart rates vary with mean 8.5 beats per five seconds and standard deviation 1 beats per five seconds. This distribution takes only whole-number values, so it is certainly not Normal.

Let x⎯hat be the mean number of beats per five seconds after measuring heart rate for 12 five-second intervals.

a. What is the standard deviation (±±0.0001) of distribution of x⎯hat according to the central limit theorem? ______beats per five seconds

b. What is the probability (±±0.0001) that x⎯hat is less than 8?

c. What is the probability (±±0.0001) that the heart rate of a runner is less than 95 beats per minute?

(Hint: restate this problem in terms of x⎯⎯hat per five seconds).

Answer 1

a.

Using the central limit theorem, the mean number of beat per 5 seconds, will have a normal distribution. The mean of this sampling distribution would be 8.5 . The standard deviation of the sampling distribution would be given by,

Thus the standard deviation of distribution of is 0.2887 beats per five seconds.

b.

The required probability would be given by,

c.

For beats per minute the mean of the distribution would be given by,

The standard deviation of the distribution would be given by,

The required probability would be given by,