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 372 minutes and standard deviation 65 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 526 minutes and standard deviation 110 minutes. A researcher records the minutes of activity for an SRS of five mildly obese people and an SRS of five lean people.a) What is the probability that the mean number of minutes of daily activity of the five mildly obese people exceeds 400 minutes? (Round your answer to four decimal places.) (b) What is the probability that the mean number of minutes of daily activity of the five lean people exceeds 400 minutes? (Round your answer to four decimal places.)

Explanation / Answer

a) For mildly obese people, Xi=400, Xbar=372, sd=65. Substitute values in following formula and obtain z score.

z=(Xi-Xbar)/s=(400-372)/65=0.43

P(X>400)=P(z>0.43)=0.3336 (area beyond z in z score table).

b) For mildly lean people, Xi=400, Xbar=526, sd=110

z=(400-526)/110=-1.15

P(X>400)=P(z>-1.15)=0.5+0.3749=0.8749 (add 0.5 to area corresponding between mean and z).

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