Is your breathing rate normal? Actually, there is no standard breathing rate for humans. It can vary from as low as 4 breaths per minute to as high as 70 or 75 for a person engaged in strenuous exercise. Suppose that the resting breathing rates for college-age students have a relative frequency distribution that is mound-shaped, with a mean equal to 12 and a standard deviation of 2.3 breaths per minute.
What fraction of all students would have breathing rates in the following intervals?
a. 9.7 to 14.3 breaths per minute
b. 7.4 to 16.6 breaths per minute
c. More than 18.9 or less than 5.1 breaths per minute

a) 68%

b) 95%

c) 0.3%

Step-by-step explanation:

Given:  

μ= Mean = 12

σ= Standard deviation = 2.3  

Since the distribution is mound-shaped, it is appropriate to use the Empirical rule.  

The Empirical Rule tells us:

Approximately 68% of the observations are within 1 standard deviation of the mean.

Approximately 95% of the observations are within 2 standard deviations of the mean.

Approximately 99.7% of the observations are within 3 standard deviations of the mean.  

(a)9.7 and 14.3 are 1 standard deviation from the mean.  

                    μ-σ=12-2.3=9.7

                    μ+σ=12+2.3=14.3

By the Empirical rule, we then note that 68% of the observations are between 9.7 and 14.3. This then implies that 68% of the students will have breathing rates between 9.7 and 14.3 breaths per minute.  

(b) 7.4 and 16.6 are 2 standard deviations from the mean.  

                      μ-2σ=12-2(2.3)=7.4

                    μ+2σ=12+2(2.3)=16.6

By the Empirical rule, we then note that 95% of the observations are between 7.4 and 16.6. This then implies that 95% of the students will have breathing rates between 7.4 and 16.6 breaths per minute.  

(c) 5.1 and 18.9 are 3 standard deviations from the mean.  

                      μ-3σ=12-3(2.3)=5.1

                    μ+3σ=12+3(2.3)=18.9

By the Empirical rule, we then note that 95% of the observations are between 5.1 and 18.9. This then implies that 99.7% of the students will have breathing rates between 5.1 and 18.9 breaths per minute.  

However, we then also know that about 100%— 99.7% = 0.3% of the students will have breathing rates less than 5.1 breaths per minute or more than 18.9 breaths per minute.  

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step-by-step explanation: