(15.30) It appears that people who are mildly obese are less active than leaner

Question

(15.30) 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 374 minutes and standard deviation 66 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 524 minutes and standard deviation 105 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 420 minutes?

B. What is the probability (±0.0001) that the mean number of minutes of daily activity of the 8 lean people exceeds 420 minutes?

Explanation / Answer

For Mildy obese people distribution is normal with mean=374 and sd=66

For lean poople distribution is normal with mean=524 and sd=105

A. For n=8, P(xbar>420) this is for mildly obese people

We will conver xbar to z with mean=374 and sd=66/sqrt(8)=23.33 (using central limit theorem)

Hence P(z>420-374/23.33)=P(z>1.97)=0.5-P(0<z<1.97)=0.5-0.4756=0.0244

B. Now here for n=8, xbar is normally distributed with mean=524 and sd=105/sqrt(8)=37.12

So P(z>420-524/37.12)=P(z>-2.80)=0.5-P(0<z<-2.80)=0.5+0.4974=0.9974

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