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 370 minutes and standard deviation 65 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with 523 minutes and standard deviation 106 minutes. A researcher records the minutes of activity for an SRS of 6 mildly obese people and an SRS of 6 lean people.

(a) What is the probability that the mean number of minutes of daily activity of the 66 mildly obese people exceeds 420420 minutes? (Enter your answer rounded to four decimal places.)

probability:

(b) What is the probability that the mean number of minutes of daily activity of the 66 lean people exceeds 420420 minutes? (Enter your answer rounded to four decimal places.)

probability:

Answer 1

a)

for normal distribution z score =(X-μ)/σx
mean μ=	370
standard deviation σ=	65.0

std error=σx̅=σ/√n=

26.54

probability =P(X>420)=P(Z>(420-370)/26.536)=P(Z>1.88)=1-P(Z<1.88)=1-0.9699=0.0301

b)

for normal distribution z score =(X-μ)/σx
mean μ=	523
standard deviation σ=	106.00

std error=σx̅=σ/√n=106/√6 =

43.27

probability that the mean number of minutes of daily activity of the6 lean people exceeds 420 minutes

probability =P(X>420)=P(Z>(420-523)/43.274)=P(Z>-2.38)=1-P(Z<-2.38)=1-0.0087=0.9913