It appears that people who are mildly obese are less active than leaner people.
ID: 3131746 • Letter: I
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 380 minutes and standard deviation 67 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 527 minutes and standard deviation 107 minutes. A researcher records the minutes of activity for an SRS of eight mildly obese people and an SRS of eight lean people.
(a) What is the probability that the mean number of minutes of daily activity of the eight mildly obese people exceeds 410 minutes? (Round your answer to four decimal places.)
(b) What is the probability that the mean number of minutes of daily activity of the eight lean people exceeds 410 minutes? (Round your answer to four decimal places.)
Explanation / Answer
a)
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 410
u = mean = 380
n = sample size = 8
s = standard deviation = 67
Thus,
z = (x - u) * sqrt(n) / s = 1.266459907
Thus, using a table/technology, the right tailed area of this is
P(z > 1.266459907 ) = 0.102674237 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 410
u = mean = 527
n = sample size = 8
s = standard deviation = 107
Thus,
z = (x - u) * sqrt(n) / s = -3.092766108
Thus, using a table/technology, the right tailed area of this is
P(z > -3.092766108 ) = 0.999008498 [ANSWER]
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