document.write( "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.
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\n" ); document.write( "Breathing rates for humans can be as low as 4 breaths per minute or as high as 70 or 75
\n" ); document.write( "for a person doing strenuous exercise. Suppose that the resting breathing rates
\n" ); document.write( "for college-age students have a distribution that is mound-shaped,
\n" ); document.write( "with a mean of 14 and a standard deviation of 2.5 breaths per minute.
\n" ); document.write( "What fraction of all students would have breathing rates in the following intervals?
\n" ); document.write( "more than 21.5 or less than 6.5 breaths per minute.
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document.write( "The problem says that the breathing rates are normally distributed.\r\n" );
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document.write( "Notice that 21.5 = 14 + 3*2.5; in other words, the upper bound of 21.5 is 3 standard deviations\r\n" );
document.write( "above the mean value.\r\n" );
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document.write( "Also notice that 6.5 = 14 - 3*2.5; in other words, the lower bound of 6.5 is 3 standard deviations\r\n" );
document.write( "below the mean value.\r\n" );
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document.write( "The relevant empirical rule says that 99.7% of data are within 3 standard deviations.\r\n" );
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document.write( "As a reference, use this link\r\n" );
document.write( "https://www.investopedia.com/terms/e/empirical-rule.asp#:~:text=The%20Empirical%20Rule%20states%20that,standard%20deviations%20from%20the%20mean.\r\n" );
document.write( "or any textbook on statistics.\r\n" );
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document.write( "Hence, only 100% - 99.7% = 0.3% of all breathing rates are more than 21.5 or less than 6.5 breaths per minute.\r\n" );
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document.write( "At this point, the problem is just solved.\r\n" );
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document.write( "ANSWER.  0.3% = 0.003 of all breathing rates are more than 21.5 or less than 6.5 breaths per minute.\r\n" );
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