Question 1205901: 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 14 and a standard deviation of 2.5 breaths per minute.
What fraction of all students would have breathing rates in the following intervals? more than 21.5 or less than 6.5 breaths per minute.
Answer by ikleyn(52776)   (Show Source):
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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 14 and a standard deviation of 2.5 breaths per minute.
What fraction of all students would have breathing rates in the following intervals?
more than 21.5 or less than 6.5 breaths per minute.
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The problem says that the breathing rates are normally distributed.
Notice that 21.5 = 14 + 3*2.5; in other words, the upper bound of 21.5 is 3 standard deviations
above the mean value.
Also notice that 6.5 = 14 - 3*2.5; in other words, the lower bound of 6.5 is 3 standard deviations
below the mean value.
The relevant empirical rule says that 99.7% of data are within 3 standard deviations.
As a reference, use this link
https://www.investopedia.com/terms/e/empirical-rule.asp#:~:text=The%20Empirical%20Rule%20states%20that,standard%20deviations%20from%20the%20mean.
or any textbook on statistics.
Hence, only 100% - 99.7% = 0.3% of all breathing rates are more than 21.5 or less than 6.5 breaths per minute.
At this point, the problem is just solved.
ANSWER. 0.3% = 0.003 of all breathing rates are more than 21.5 or less than 6.5 breaths per minute.
Solved.
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