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 365 minutes and standard deviation 69 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with 528 minutes and standard deviation 106 minutes. A researcher records the minutes of activity for an SRS of 66 mildly obese people and an SRS of 66 lean people.

(a) What is the probability that the mean number of minutes of daily activity of the 66 mildly obese people exceeds 420 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 420 minutes? (Enter your answer rounded to four decimal places.)

probability:

Answer 1

Solution :

(a)

Given that ,

mean = = 365

standard deviation = = 69

P(x > 420) = 1 - P(x < 420)

= 1 - P((x - ) / < (420 - 365 / 69)

= 1 - P(z < 0.7971)

= 1 - 0.7873

= 0.2127

Probability = 0.2127

(b)

Given that ,

mean = = 528

standard deviation = = 106

P(x > 420) = 1 - P(x < 420)

= 1 - P((x - ) / < (420 - 528) / 106)

= 1 - P(z < -1.0189)

= 1 - 0.1541

= 0.8459

P(x > 420) = 0.8459

Probability = 0.8459