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 375 minutes and standard deviation 69 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 526 minutes and standard deviation 106 minutes. A researcher records the minutes of activity for an SRS of 5 mildly obese people and an SRS of 5 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 5 mildly obese people exceeds 420 minutes? What is the probability (±0.0001) that the mean number of minutes of daily activity of the 5 lean people exceeds 420 minutes?
a)
| for normal distribution z score =(X-μ)/σx | |
| here mean= μ= | 375 |
| std deviation =σ= | 69.0000 |
| sample size =n= | 5 |
| std error=σx̅=σ/√n= | 30.8577 |
probability that the mean number of minutes of daily activity of the 5 mildly obese people exceeds 420 minutes:
| probability = | P(X>420) | = | P(Z>1.458)= | 1-P(Z<1.46)= | 1-0.9279= | 0.0721 |
b)
| here mean= μ= | 526 |
| std deviation =σ= | 106.0000 |
| sample size =n= | 5 |
| std error=σx̅=σ/√n= | 47.4046 |
probability that the mean number of minutes of daily activity of the 5 lean people exceeds 420 minutes
| probability = | P(X>420) | = | P(Z>-2.236)= | 1-P(Z<-2.24)= | 1-0.0125= | 0.9875 |
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