It appears that people who are mildly obese are less active than leaner people.

Question

It appears that 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, the mean number of minutes of daily activity (standing or walking) is approximately Normally distributed with mean 377 minutes and standard deviation 67 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 520 minutes and standard deviation 108 minutes. A researcher records the minutes of activity for an SRS of 8 mildly obese people and an SRS of 8 lean people.

Use z-scores rounded to two decimal places to answer the following:

a. What is the probability (±±0.0001) that the mean number of minutes of daily activity of the 8 mildly obese people exceeds 420400410 minutes?

b. What is the probability (±±0.0001) that the mean number of minutes of daily activity of the 8 lean people exceeds 420400410 minutes?

Explanation / Answer

Solution:-

a.)Among mildly obese people, the mean is 377 minutes and the standard deviation is 67 minutes

Mean = 377

Standard deviation = 67

Standard error / n = 67 / 8 = 23.6880

standardize xbar to z = (xbar - ) / ( / n )

P(xbar > 420400410) = P( z > ( 420400410-377) / 23.6880)

= P(z > 17747384.0341) = 0.00 (from normal probability table)

b) Among lean people, the mean is 520 minutes and the standard deviation is 108 minutes
Mean = 520
Standard deviation = 108
Standard error / n = 108 / 8 = 38.1838
standardize xbar to z = (xbar - ) / ( / n )
P(xbar > 420400410) = P( z > (420400410-520) / 38.1837)
= P(z > 11009930.6772) = 0.0000
(from normal probability table)

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