Question

Body mass index (BMI) in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2. Answer the following questions: a) A BMI between 25 and 30 is considered overweight. What proportion of children are overweight? b) A BMI of 30 or more is considered obese. What proportion of children are obese? c) In a random sample of 10 children, what is the probability that their mean BMI exceeds 25?

Answer 1

X: Body mass index (BMI) in children

X ~ N (24.5 , 6.2)

mean () = 24.5

population sd () = 6.2

a). the proportion of students who are in between BMI 25 and 30 be:-

[ from standard normal table]

= 0.2814

so, proportion of children are overweight = 0.2814

b).the proportion of students who have BMI 30 or more be:-

[ from standard normal table]

= 0.1867

the proportion of children are obese = 0.1867

c). for a sample of 10 students,

the sample mean ()be = = 24.5

the sample sd (s) be = = 1.96

the probability that their mean BMI exceeds 25 be:-

= 1 - 0.6026 [ from standard normal table]

= 0.3974

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