Answer:
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.
