Question

2. Suppose body mass index (BMI) varies approximately to the normal distribution in a population of boys aged 2-20 years. A national survey analyzed the BMI for American adolescents in this age range and found the µ=17.8 and the ?=1.9. a) What is the 25th percentile of this distribution? (1 point) b) What is the z-score corresponding to finding a boy with at least a BMI of 19.27? (2 points) c) What is the probability of finding a boy with at least this BMI? (2 points)

Answer 1

Solution:

Given that,

= 17.8

= 1.9

a ) P(Z < z) = 25%

P(Z < z) = 0.25

P(Z < - 0.6745) = 0.25

z = - 0.6745

Using z-score formula,

x = z * +

x = - 0.6745 * 1.9 + 17.8 = 16.5185

The sample mean is 16.52

b ) P ( x   19.27 )

= 1 - P ( X   19.27 )

= 1 - p ( X-  /   ) ( 19.27- 17.8 / 1.9 )

= 1 - p ( z < 1.47 / 1.9)

= 1 - p ( z < 0.77 )

Using z table

= 1 - 0.7793

= 0.2207

Probability = 0.2207

c) The Probability is 0.2207