Question

A) Let X equal the distribution of the possible BMIs in children with reported weight problems aged 5-18 years old. Suppose this distribution was approximately normal with mean of 21.7 and standard deviation of 1.34.

• The proportion of children aged 5-18 years old with BMI between 21 and 23 is: a) 0.5325 b) 0.5359 c) 0.6 d) 0.5486 e) none of the above

B) What BMI level correspond to the top 8%? a) 1.41 b) 10.22 c) 23.89 d) 23.6 e) none of the above

Answer 1

Solution :

A)

P(21 < x < 23) = P[(21 - 21.7)/ 1.34) < (x - ) /  < (23 - 21.7) / 1.34) ]

= P(-0.52 < z < 0.97)

= P(z < 0.97) - P(z < -0.52)

= 0.834 - 0.3015

= 0.5325

proportion = 0.5325

option a) is correct

B)

Using standard normal table ,

P(Z > z) = 8%

1 - P(Z < z) = 0.08

P(Z < z) = 1 - 0.08

P(Z < 1.41) = 0.92

z = 1.41

Using z-score formula,

x = z * +

x = 1.41 * 1.34 + 21.7 = 23.6

level = 23.6

option d) is correct