Question

Suppose the distribution of BMI (kg/m2) among a group of diabetic children varies normally with a mean of 26.8 and a σ=3.7.

A) What is the probability of randomly selecting an obese child (BMI>30) based on a sample of 15 children?

B) What is the probability of randomly selecting a “normal” child with a BMI between 18.5 and 24.9?

Answer 1

Solution :

Given that,

mean = = 26.8

standard deviation = = 3.7

n = 10

= 26.8

₌ / n = 3.7 15 =0.9553

A ) P (   > 30)

= 1 - P ( < 30 )

= 1 - P ( - /) < 30 - 26.8 /0.9553 )

= 1 - P( z <  3.2 / 0.9553 )

= 1 - P ( z < 3.35 )   

Using z table

= 1 - 0.9996

= 0.0004

Probability = 0.0004

B ) P (18.5 < x < 24.9 )

P ( 18.5 - 26.8 /3.7 ) < ( x -  / ) < ( 24.9 - 26.8 /3.7 )

P ( - 8.3 / 3.7 < z < -1.9 / 3.7 )

P ( -2.24 < z < -0.51 )

P ( z < -0.51 ) - P ( z < -2.24 )

Using z table

= 0.3050 - 0.0125

= 0.2925

Probability = 0.2925