The following table shows the distribution of BMI in children living in US and E

ID: 3238168 • Letter: T

Question

The following table shows the distribution of BMI in children living in US and European urban neighborhoods. (The data are in millions.)

If a child is selected at random,

a. What is the probability they are overweight?

b. What is the probability that a child is overweight if they live in the USA?

c. What is the probability that a child is overweight if they live in Europe?

d. What is the probability that a child lives in a US neighborhood and is obese?

e. Are overweight and neighborhood location exclusive events? Why or why not?

2. BMI in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 5.7.

a. A BMI between 25 and 30 is considered overweight. What it the probability of randomly picking a child who is overweight?

b. A BMI of 30 or more is considered obese. What proportion of children are obese?

c. What percentage of children are considered normal/underweight (BMI less than 25)?

d. Imagine taking a sample of 9 children. How much error would you expect to find between the sample and the population (what is the SE)?

e. What is the probability of selecting 9 children who, on average, are considered obese (BMI greater than 30)?

f. (Bonus) Why is there a difference between the answers in b and e?

Neighborhood Normal weight Overweight Obese US 120 35 50 EUROPE 106 47 21

Sum of all the data in the table = 379

(a) Probability = (35 + 47)/379 = 0.2164

(b) Probability = 35/(120 + 35 + 50) = 0.1707

(d) Probability = 50/379 = 0.1319

(e) No, because there are people who are overweight and live in a particular neighborhood.

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