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 371 minutes and standard deviation 65 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 528 minutes and standard deviation 108 minutes. A researcher records the minutes of activity for an SRS of 6 mildly obese people and an SRS of 6 lean people.Use z-scores rounded to two decimal places to answer the following:What is the probability

Answer 1

Question Continuation

What is the probability of people who are

1. mildly obese

2. lean

One study looked at the average, 0.0001) that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes?

Answer:

1. 0.0322

2. 0.9929

Step-by-step explanation:

Given

n = 6

For midly obese people

Mean, u = 371

Standard Deviation, σ = 65

For lean people

Mean, u = 528

Standard Deviation, σ = 108

1. Calculating the probability that people who are mildly obese .

Using z scores for these probabilities.

z = (x - u)/(σ/√n)

Where x = 420

For midly obese people,

z =(420-371)/(65/√6)

z = 1.84653842148270348941026

z = 1.85 --- Approximated

Using the z table, the probability of midly obese people = 1 - p(z=1.85)

= 1 - 0.9678

= 0.0322

2. Calculating the probability that people who are lean

x = 420

z = (420 - 528)/(108/√6)

z = −2.4494897427831780981972

z = -2.45 --- Approximated

Using the z table, the probability of midly obese people = 1 - p(-2.45)

= 1 - 0.0071

= 0.9929