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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.