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Use the empirical rule to answer the following question.

in an experiment, 200 runners were asked to run for 6 minutes on a treadmill. their heart rates after 6 minutes were normally distributed, with a mean of 110 bpm and a standard deviation of 10 bpm.

a. what percent of the runners had heart rates between 100 and 120 bpm?

b. what percent of the runners had heart rates between 110 and 130 bpm?

c. what percent of the runners had heart rates over 90 bpm?

Respuesta :

Using the Empirical Rule, it is found that the percentages are given as follows:

a) 68%.

b) 47.5%.

c) 97.5%.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

  • Approximately 68% of the measures are within 1 standard deviation of the mean.
  • Approximately 95% of the measures are within 2 standard deviations of  the mean.
  • Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Item a:

Both within 1 standard deviation of the mean, hence 68%.

Item b:

Between the mean and two standard deviations above the mean, hence 95% of 50%(as the normal distribution is symmetric), hence:

P = 95% x 0.5 = 47.5%.

Item c:

Two standard deviations below the mean and below, hence only the bottom 5/2 = 2.5% is removed, so 97.5%.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

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