Question

Breathing rates for humans can be as low as 4 breaths per minute or as high as 70 or 75 for a person doing strenuous exercise. Suppose that the resting breathing rates for college-age students have a distribution that is mound-shaped, with a mean of 13 and a standard deviation of 1.3 breaths per minute. What fraction of all students have breathing rates in the following intervals? What fraction of all students would have breathing rates in the following intervals? (a) 11.7 to 14.3 breaths per minute (b) 10.4 to 15.6 breaths per minute (c) more than 16.9 or less than 9.1 breaths per minute

Answer 1

Given mean u =13 and standard deviation o =1.3 ( One sigma limits are 13+11.3)(11.7, 14.3) Two sigma limits are (2(1321.3) (10.4, 15.6) -- (30(13+31.3) (9.1, 16.9) Three sigma limits are a) Given limits are 1 sigma limits Using the Empirical rule 68% of the data fall between 1 sigma limits Required fraction is 68% or 17/25 b) Given limits are 2 sigma limits Using the Empirical rule 95% of the data fall between 2 sigma limits Required fraction is 95% or 19/20 c) Given limits are 3 sigma limits Using the Empirical rule 99.7% of the data fall between 3 sigma limits (100-99.7)%0.3% of the data fall outside of the 3 sigma limits Required fraction is 0.3% or 3/10