Answer:
Obese people
![Lower = \mu - 2\sigma = 373- 2(67) = 239](https://tex.z-dn.net/?f=%20Lower%20%3D%20%5Cmu%20-%202%5Csigma%20%3D%20373-%202%2867%29%20%3D%20239)
![Upper = \mu + 2\sigma = 373+ 2(67) = 507](https://tex.z-dn.net/?f=%20Upper%20%3D%20%5Cmu%20%2B%202%5Csigma%20%3D%20373%2B%202%2867%29%20%3D%20507)
Lean People
![Lower = \mu - 2\sigma = 526- 2(107) = 312](https://tex.z-dn.net/?f=%20Lower%20%3D%20%5Cmu%20-%202%5Csigma%20%3D%20526-%202%28107%29%20%3D%20312)
![Upper = \mu + 2\sigma = 526+ 2(107) = 740](https://tex.z-dn.net/?f=%20Upper%20%3D%20%5Cmu%20%2B%202%5Csigma%20%3D%20526%2B%202%28107%29%20%3D%20740)
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, "almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ)".
Solution to the problem
Obese people
Let X the random variable that represent the minutes of a population (obese people), and for this case we know the distribution for X is given by:
Where
and
On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:
![Lower = \mu - 2\sigma = 373- 2(67) = 239](https://tex.z-dn.net/?f=%20Lower%20%3D%20%5Cmu%20-%202%5Csigma%20%3D%20373-%202%2867%29%20%3D%20239)
![Upper = \mu + 2\sigma = 373+ 2(67) = 507](https://tex.z-dn.net/?f=%20Upper%20%3D%20%5Cmu%20%2B%202%5Csigma%20%3D%20373%2B%202%2867%29%20%3D%20507)
Lean People
Let X the random variable that represent the minutes of a population (lean people), and for this case we know the distribution for X is given by:
Where
and
On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:
![Lower = \mu - 2\sigma = 526- 2(107) = 312](https://tex.z-dn.net/?f=%20Lower%20%3D%20%5Cmu%20-%202%5Csigma%20%3D%20526-%202%28107%29%20%3D%20312)
![Upper = \mu + 2\sigma = 526+ 2(107) = 740](https://tex.z-dn.net/?f=%20Upper%20%3D%20%5Cmu%20%2B%202%5Csigma%20%3D%20526%2B%202%28107%29%20%3D%20740)
The interval for the lean people is significantly higher than the interval for the obese people.