It appears to people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, minutes of activity varied according to the N(373,67) distribution. Minutes of activity for lean people had the N(526,107) distribution. Within what limits do the active minutes for 95% of the people in each group fall? Use the 68-95-99.7 rule.
I have no idea where to even begin to try and answer this. I am so lost. Please help!! Thanks!
About 95% of a normal distribution lies within 2 standard deviations of the mean.
N(373,67) means the distribution is a normal distribution with mean = 373 and the variance = 67 (standard deviation = square root of 67).
N(526,107) means the distribution is a normal distribution with mean = 526 and the variance = 107 (standard deviation = square root of 107).
Determine the limits by using the mean and standard deviation. Remember to determine 2 standard deviations below the mean and 2 standard deviations above the mean for your limits.
I'll let you take it from here.
N(373,67) means the distribution is a normal distribution with mean = 373 and the variance = 67 (standard deviation = square root of 67).
To determine the limits within which the active minutes fall for 95% of the people in each group, we can use the 68-95-99.7 rule.
The 68-95-99.7 rule (also known as the empirical rule) states that for data following a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, we have two distributions: N(373,67) for mildly obese people and N(526,107) for lean people.
For the N(373,67) distribution (mildly obese people):
Mean = 373
Standard Deviation = 67
To find the limits within which 95% of the data falls:
1. Calculate one standard deviation:
Lower Limit = Mean - (1 * Standard Deviation)
Upper Limit = Mean + (1 * Standard Deviation)
2. Calculate two standard deviations:
Lower Limit = Mean - (2 * Standard Deviation)
Upper Limit = Mean + (2 * Standard Deviation)
For the N(526,107) distribution (lean people):
Mean = 526
Standard Deviation = 107
Repeat the same steps as above to find the limits within which 95% of the data falls.
Thus, the limits for 95% of the people in each group are as follows:
- For mild obese people: Within one standard deviation, or within two standard deviations, of the mean from the N(373,67) distribution.
- For lean people: Within one standard deviation, or within two standard deviations, of the mean from the N(526,107) distribution.
Keep in mind that these limits are approximate as they are based on the 68-95-99.7 rule.