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 371 minutes and standard deviation 69 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with 526 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 6 mildly obese people exceeds 410 minutes? (Enter your answer rounded to four decimal places.)

(b) What is the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 410 minutes? (Enter your answer rounded to four decimal places.)

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	371
std deviation   =σ=	69.000
sample size       =n=	6
std error=σx̅=σ/√n=	28.16913

probability =P(X>410)=P(Z>(410-371)/28.169)=P(Z>1.38)=1-P(Z<1.38)=1-0.9162=0.0838

b)

here mean=       μ=	526
std deviation   =σ=	106.000
sample size       =n=	6
std error=σx̅=σ/√n=	43.27432

probability =P(X>410)=P(Z>(410-526)/43.274)=P(Z>-2.68)=1-P(Z<-2.68)=1-0.0037=0.9963