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 365 minutes and standard deviation 69 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 527 minutes and standard deviation 104 minutes. A researcher records the minutes of activity for an SRS of 6 mildly obese people and an SRS of 6 lean people.

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

What is the probability (±±0.0001) that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 400 minutes?

What is the probability (±±0.0001) that the mean number of minutes of daily activity of the 6 lean people exceeds 400 minutes?

Explanation / Answer

Here for mildly obese people mean=365 abd sd=69

So P(xbar>400)=P(z>400-365/(69/sqrt(6))=P(z>1.24)=0.1075

Now for lean peple mean=527 and sd-104

So P(xbar>400)=P(400-527/(104/sqrt(6))=P(z>-2.99)=0.9986

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